Prove: Product of Sin Values = $\frac{\sqrt{n}}{2^{n-1}}$

[Dragonfall]

Homework Statement

Show that $$\prod_{k=1}^{n-1}\sin\frac{k\pi}{2n}=\frac{\sqrt{n}}{2^{n-1}}$$

The Attempt at a Solution

I have no idea where to start.

 

[morphism]

Let $\zeta$ be the primitive (2n)th root of unity, i.e. $\zeta = \exp(\pi i / n)$. Try to simplify $|1 - \zeta^k|$ (where k is some positive integer). Then try playing around with x^(2n) - 1.