Trigonometric identity between sines of multiples of $\pi/70$ [duplicate]

Prove that:

$$\left(\sin\frac {9\pi}{70}+ \sin\frac {29\pi}{70} - \sin\frac {31\pi}{70}\right) \left(\sin\frac {\pi}{70}-\sin\frac {11\pi}{70} - \sin\frac {19\pi}{70}\right) =\frac {\sqrt {5} -4}{4}$$

use the following identity $$\sin x={\frac {e^{ix}-e^{-ix}}{2i}}$$