Sine of Integer Multiple of Argument/Formulation 8/Examples/Sine of Quintuple Angle

Example of Use of Sine of Integer Multiple of Argument/Formulation 8

 * $\map \sin {5 \theta } = \map \sin {4 \theta} \paren { 2 \cos \theta - \cfrac 1 {2 \cos \theta - \cfrac 1 {2\cos \theta - \cfrac 1 {2 \cos \theta } } } }$

Proof
Follows directly from the Sine of Integer Multiple of Argument/Formulation 8:

Explicit derivation illustrated below: