Cosine of Integer Multiple of Argument

Theorem
For $n \in \Z_{>0}$:
 * $\cos n \theta = \dfrac 1 2 \left({\left({2 \cos \theta}\right)^n - \dfrac n 1 \left({2 \cos \theta}\right)^{n - 2} + \dfrac n 2 \dbinom {n - 3} 1 \left({2 \cos \theta}\right)^{n - 4} - \dfrac n 3 \dbinom {n - 4} 2 \left({2 \cos \theta}\right)^{n - 6}\cdots + \cdots}\right)$

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