Quadruple Angle Formulas/Cosine/Factor Form

Theorem

 * $\cos 4 \theta = \paren {\cos \theta - \cos \dfrac \pi 8} \paren {\cos \theta - \cos \dfrac {3 \pi} 8} \paren {\cos \theta - \cos \dfrac {5 \pi} 8} \paren {\cos \theta - \cos \dfrac {7 \pi} 8}$

Proof
Setting $z = e^{i \theta}$: