\[= \frac{\sqrt{3}}{4} - \frac{1}{2}\sin{8{^\circ}} + \frac{1}{4} + \frac{1}{2}\sin{8{^\circ}} =\]
\[= \frac{\sqrt{3}}{4} + \frac{1}{4} = \frac{\sqrt{3} + 1}{4}\]