Trigonometric Ratios And Identities

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

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

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

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