Sine of 36 Degrees

Theorem

 * $\sin 36^\circ = \sin \dfrac \pi 5 = \dfrac {\sqrt {\sqrt 5 / \phi} } 2 = \sqrt {\dfrac 5 8 - \dfrac {\sqrt 5} 8}$

where $\phi$ denotes the golden mean.

Proof
We also have: