Cosine of Integer Multiple of Argument/Formulation 5/Examples/Cosine of Sextuple Angle

Example of Use of Cosine of Integer Multiple of Argument: Formulation $5$

 * $\map \cos {6 \theta } = -1 + 2 \cos \theta \paren {\cos 5 \theta - \cos 3 \theta + \cos \theta }$

Proof
Follows directly from the Cosine of Integer Multiple of Argument: Formulation $5$:

Explicit derivation illustrated below: