$$( \sin p i f ) : \frac { a ^ { 2 } + b } { a ^ { 2 } - b } + \frac { a ^ { 2 } - b } { a ^ { 2 } + b } - \frac { a ^ { 4 } + b ^ { 2 } } { a ^ { 4 } - b ^ { 2 } }$$
$\frac{a^{4}\sin(\pi f)+b^{2}\sin(\pi f)-2ba^{2}\sin(\pi f)-2ba^{2}}{a^{4}-b^{2}}$
$\left(b\neq a^{2}\text{ and }b>0\text{ and }|a|\neq \sqrt{b}\right)\text{ or }\left(b\neq -a^{2}\text{ and }b<0\text{ and }|a|\neq \sqrt{-b}\right)\text{ or }\left(|b|\neq a^{2}\text{ and }|a|\neq \sqrt{b}\text{ and }|a|\neq \sqrt{-b}\right)$
$-\frac{4ab\left(-a^{4}\sin(\pi f)-b^{2}\sin(\pi f)+2ba^{2}\sin(\pi f)-a^{4}-b^{2}\right)}{\left(a^{4}-b^{2}\right)^{2}}$
$\left(b\neq a^{2}\text{ and }b>0\text{ and }|a|\neq \sqrt{b}\right)\text{ or }\left(b\neq -a^{2}\text{ and }b<0\text{ and }|a|\neq \sqrt{-b}\right)\text{ or }\left(|b|\neq a^{2}\text{ and }|a|\neq \sqrt{b}\text{ and }|a|\neq \sqrt{-b}\right)$
