# Thread: nth roots of unity?

1. ## nth roots of unity?

If 1, $\alpha_1,\alpha_2,\alpha_3,\mbox{...}\alpha_{n - 1}$ are the $n^{th}$ roots of unity, prove that:
$\sin\frac{\pi}{n}\sin\frac{2\pi}{n}\sin\frac{3\pi} {n}\mbox{...}\sin\frac{(n - 1)\pi}{n} = \frac{n}{2^{n - 1}}$