Sine of Integer Multiple of Argument/Formulation 7/Examples/Sine of Quintuple Angle

Example of Use of Sine of Integer Multiple of Argument/Formulation 7

 * $\map \sin {5 \theta } = \map \sin {\theta} + 2 \sin \theta \paren { \cos 4 \theta + \cos 2 \theta }$

Proof
Follows directly from the Sine of Integer Multiple of Argument/Formulation 7:

Explicit derivation illustrated below: