How to express the equations as the Square root Like? $$2\sin \frac{\pi}{16}= \sqrt{2-\sqrt{2+\sqrt{2}}}$$
What law is need to be applied here? Do I have to make the $\frac{\pi}{16}$ in a form  that will be give us $\sqrt{2}$ like  sin 45 degree? 

Call $x = \sin \frac{\pi}{16} \to 1-2x^2 = \cos \frac{\pi}{8} \to \left(1-2x^2\right)^2 = \cos^2 \frac{\pi}{8} = \dfrac{1+\cos \frac{\pi}{4}}{2} = \dfrac{2+\sqrt{2}}{4} \to 1-2x^2 = \dfrac{\sqrt{2+\sqrt{2}}}{2} \to x^2 = \dfrac{2-\sqrt{2+\sqrt{2}}}{4} \to 2x = \sqrt{2-\sqrt{2+\sqrt{2}}}$.
