\begin{multline*}
\begin{tikzpicture}[baseline,rotate=90,scale=.9]
	\node at (0,0) [rectangle,draw, fill=white] {$ \JW{3} $};
	\node at (2,0)  [rectangle,draw, fill=white]  {$ \JW{1} $};
   \begin{pgfonlayer}{background}	
	\draw (4,0) arc (0:180:2cm);
	\draw (3.8,0) arc (0:180:1.8cm);
	\draw (4.2,0) arc (0:180:2.2cm);	
	\draw[line width=4pt,white,opaque] (2.1,0) arc (0:90:2.1cm);
	\draw (2.1,0) arc (0:180:2.1cm);
	\draw (2.1,0) arc (0:-180:2.1cm);
	\draw[line width=4pt,white,opaque] (0,0) arc (-180:-90:2cm);
	\draw[line width=4pt,white,opaque] (0.2,0) arc (-180:-90:1.8cm);
	\draw[line width=4pt,white,opaque] (-.2,0) arc (-180:-90:2.2cm);			
	\draw (4,0) arc (0:-180:2cm);
	\draw (3.8,0) arc (0:-180:1.8cm);
	\draw (4.2,0) arc (0:-180:2.2cm);	
   \end{pgfonlayer}
\end{tikzpicture}
=\frac{\qi{3}}{\qi{7}}
\begin{tikzpicture}[baseline,rotate=90,scale=.9]
	\node at (0,0) [rectangle,draw, fill=white] {$ \JW{3} $};
	\node at (20:2.1cm)  [ellipse,draw, fill=white,minimum height=.8cm]  {$^\star S \;$};
	\node at (-20:2.1cm)  [ellipse,draw, fill=white,minimum height=.8cm]  {$\; S^\star $};
   \begin{pgfonlayer}{background}	
	\draw (4,0) arc (0:180:2cm);
	\draw (3.8,0) arc (0:180:1.8cm);
	\draw (4.2,0) arc (0:180:2.2cm);
	\draw[line width=4pt,white,opaque] (2.1,0) arc (0:90:2.1cm);
	\draw (2.1,0) arc (0:180:2.1cm);
	\draw (2.1,0) arc (0:-180:2.1cm);
	\draw (-20:1.9cm) arc (-20:20:1.9);
	\draw (-20:2.3cm) arc (-20:20:2.3);
	\draw[line width=4pt,white,opaque] (0,0) arc (-180:-90:2cm);
	\draw[line width=4pt,white,opaque] (0.2,0) arc (-180:-90:1.8cm);
	\draw[line width=4pt,white,opaque] (-.2,0) arc (-180:-90:2.2cm);
	\draw (4,0) arc (0:-180:2cm);
	\draw (3.8,0) arc (0:-180:1.8cm);
	\draw (4.2,0) arc (0:-180:2.2cm);	
   \end{pgfonlayer}
\end{tikzpicture} 
=\frac{\qi{3}}{\qi{7}}
\begin{tikzpicture}[baseline,rotate=90,scale=.9]
	\node at (0,0) [rectangle,draw, fill=white] {$ \JW{3} $};
	\node at (20:2.1cm)  [ellipse,draw, fill=white,minimum height=.8cm]  {$^\star S \; $};
	\node at (-180:2.1cm)  [ellipse,draw, fill=white,minimum height=.8cm,rotate=180]  {$\; S^\star$};
   \begin{pgfonlayer}{background}	
	\draw (4,0) arc (0:180:2cm);
	\draw (3.8,0) arc (0:180:1.8cm);
	\draw (4.2,0) arc (0:180:2.2cm);
	\draw[line width=4pt,white,opaque] (2.1,0) arc (0:90:2.1cm);
	\draw (2.1,0) arc (0:180:2.1cm);
	\draw (2.1,0) arc (0:-180:2.1cm);
	\draw (1.9,0) arc (0:-180:1.9cm);
	\draw (1.9,0) arc (0:20:1.9cm);
	\draw (20:1.7cm) arc (20:-180:1.7);
	\draw[line width=4pt,white,opaque] (0,0) arc (-180:-90:2cm);
	\draw[line width=4pt,white,opaque] (0.2,0) arc (-180:-90:1.8cm);
	\draw[line width=4pt,white,opaque] (-.2,0) arc (-180:-90:2.2cm);		
	\draw (4,0) arc (0:-180:2cm);
	\draw (3.8,0) arc (0:-180:1.8cm);
	\draw (4.2,0) arc (0:-180:2.2cm);	
   \end{pgfonlayer}
\end{tikzpicture}\\
=-\frac{\qi{3}}{\qi{7}}
\begin{tikzpicture}[baseline,rotate=90,scale=.9]
	\node at (0,0) [rectangle,draw, fill=white] {$ \JW{3} $};
	\node at (-20:2.1cm)  [ellipse,draw, fill=white,minimum height=.8cm]  {$^\star S \;$};
	\node at (20:2.1cm)  [ellipse,draw, fill=white,minimum height=.8cm]  {$\;  S^\star$};
   \begin{pgfonlayer}{background}	
	\draw (4,0) arc (0:180:2cm);
	\draw (3.8,0) arc (0:180:1.8cm);
	\draw (4.2,0) arc (0:180:2.2cm);
	\draw[line width=4pt,white,opaque] (2.1,0) arc (0:90:2.1cm);
	\draw[line width=4pt,white,opaque] (1.9,0) arc (0:90:1.9cm);
	\draw[line width=4pt,white,opaque] (1.7,0) arc (0:90:1.7cm);	
	\draw (1.9,0) arc (0:180:1.9cm);
	\draw (20:2.1cm) arc (20:180:2.1cm);
	\draw (20:1.7cm) arc (20:180:1.7cm);
	\draw (1.9,0) arc (0:-180:1.9cm);
	\draw (-20:2.1cm) arc (-20:-180:2.1cm);
	\draw (-20:1.7cm) arc (-20:-180:1.7cm);
	\draw[line width=4pt,white,opaque] (0,0) arc (-180:-90:2cm);
	\draw[line width=4pt,white,opaque] (0.2,0) arc (-180:-90:1.8cm);
	\draw[line width=4pt,white,opaque] (-.2,0) arc (-180:-90:2.2cm);	
	\draw (4,0) arc (0:-180:2cm);
	\draw (3.8,0) arc (0:-180:1.8cm);
	\draw (4.2,0) arc (0:-180:2.2cm);	
   \end{pgfonlayer}
\end{tikzpicture}
=-
\begin{tikzpicture}[baseline,rotate=90,scale=.9]
	\node at (0,0) [rectangle,draw, fill=white] {$ \JW{3} $};
	\node at (0:1.9cm)  [rectangle,draw, fill=white,minimum height=.8cm]  {$\JW{3}$};
   \begin{pgfonlayer}{background}	
	\draw (4,0) arc (0:180:2cm);
	\draw (3.8,0) arc (0:180:1.8cm);
	\draw (4.2,0) arc (0:180:2.2cm);
	\draw[line width=4pt,white,opaque] (2.1,0) arc (0:90:2.1cm);
	\draw[line width=4pt,white,opaque] (1.9,0) arc (0:90:1.9cm);
	\draw[line width=4pt,white,opaque] (1.7,0) arc (0:90:1.7cm);	
	\draw (2.1,0) arc (0:180:2.1cm);
	\draw (1.9,0) arc (0:180:1.9cm);
	\draw (0:1.7cm) arc (0:180:1.7cm);
	\draw (2.1,0) arc (0:-180:2.1cm);
	\draw (1.9,0) arc (0:-180:1.9cm);
	\draw (0:1.7cm) arc (0:-180:1.7);
	\draw[line width=4pt,white,opaque] (0,0) arc (-180:-90:2cm);
	\draw[line width=4pt,white,opaque] (0.2,0) arc (-180:-90:1.8cm);
	\draw[line width=4pt,white,opaque] (-.2,0) arc (-180:-90:2.2cm);		
	\draw (4,0) arc (0:-180:2cm);
	\draw (3.8,0) arc (0:-180:1.8cm);
	\draw (4.2,0) arc (0:-180:2.2cm);	
   \end{pgfonlayer}
\end{tikzpicture}
\end{multline*}