Triple Angle Formulas/Cosine/2 cos 3 theta + 1

Theorem

 * $2 \cos 3 \theta + 1 = \paren {\cos \theta - \cos \dfrac {2 \pi} 9} \paren {\cos \theta - \cos \dfrac {4 \pi} 9} \paren {\cos \theta - \cos \dfrac {8 \pi} 9}$

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