$\frac{1}{16}\left[\sin \frac{\pi}{7}+\sin \frac{2 \pi}{7}+\sin \frac{3 \pi}{7}\right]$

$\frac{1}{8}\left[\sin \frac{2 \pi}{7}+\sin \frac{3 \pi}{7}-\sin \frac{\pi}{7}\right]$

$\frac{1}{32}\left[\sin \frac{2 \pi}{7}+\sin \frac{3 \pi}{7}-\sin \frac{\pi}{7}\right]$

$\frac{1}{32}\left[\sin \frac{\pi}{7}-\sin \frac{2 \pi}{7}+\sin \frac{3 \pi}{7}\right]$

-13

-6

$-\frac{1734}{169}$

13

-26

26

1

-1

$-4 \sin \frac{A+B}{2} \cos \frac{A+C}{2} \sin \frac{A+D}{2}$

$4 \sin \frac{A+B}{2} \sin \frac{A+C}{2} \sin \frac{A+D}{2}$

$-4 \sin \frac{A+B}{2} \sin \frac{A+C}{2} \sin \frac{A+D}{2}$

$4 \sin \frac{A+B}{2} \cos \frac{A+C}{2} \sin \frac{A+D}{2}$