Product Formula for Sine

Theorem

 * $\displaystyle \sin \left({n z}\right) = 2^{n-1} \prod_{k \mathop = 0}^{n-1} \sin \left({z + \frac{k \pi} n}\right)$

Corollary

 * $\displaystyle \prod_{k \mathop = 1}^{n-1} \sin \left({\frac {k \pi} n}\right) = 2^{1-n} n$