Cosine of Integer Multiple of Argument

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

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