Sine of Integer Multiple of Argument/Formulation 9/Examples/Sine of Quintuple Angle

Example of Use of Sine of Integer Multiple of Argument/Formulation 9

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

Proof
Follows directly from the Sine of Integer Multiple of Argument/Formulation 9:

Explicit derivation illustrated below: