Sine of 3 Degrees

Theorem

 * $\sin 3^\circ = \sin \dfrac {\pi} {60} = \dfrac{ \sqrt{30} + \sqrt{10} - \sqrt 6 - \sqrt 2 - 2\sqrt {15 + 3 \sqrt5 } + 2\sqrt {5 + \sqrt5 } }{16}$

where $\sin$ denotes the sine function.