Hi! I have stuck in this problem for almost an hour, it is from a textbook:

Prove that

$\displaystyle \displaystyle \sin \frac{\pi}{27}\sin \frac{2\pi}{27}\sin \frac{3\pi}{27} \cdots \sin \frac{13\pi}{27}=\frac{3\sqrt{3}}{2^{13}}$

Any help will be appreciated!!