\[\sin{15{^\circ}} = \sqrt{\frac{1 - \cos{30{^\circ}}}{2}} =\]
\[= \sqrt{\frac{1 - \frac{\sqrt{3}}{2}}{2}} = \sqrt{\frac{2 - \sqrt{3}}{4}} =\]
\[= \sqrt{\frac{2 - \sqrt{3}}{2}}\]