Sine of Integer Multiple of Argument/Formulation 1

Theorem
For $n \in \Z_{>0}$:
 * $\displaystyle \sin n \theta = \sin \theta \left({\left({2 \cos \theta}\right)^{n-1} - \binom {n - 2} 1 \left({2 \cos \theta}\right)^{n-3} + \binom {n - 3} 2 \left({2 \cos \theta}\right)^{n-5} - \cdots}\right)$

That is:
 * $\displaystyle \sin n \theta = \sin \theta \left({\sum_{k \ge 0} \left({-1}\right)^k \binom {n - \left({k + 1}\right)} k \left({2 \cos \theta}\right)^{n - \left({2 k + 1}\right)}}\right)$