Odd Multiple Angle Formula for Sine

Theorem

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

for $\sin \theta \ne 0$.