Formulaes for finding the solution for half-angle trigonometric equations:
\begin{align} \sin \frac{\alpha}{2} &= \pm \sqrt{\frac{1- \cos \alpha }{2}} \\ \\ \cos \frac{\alpha}{2} &= \pm \sqrt{\frac{1+ \cos \alpha }{2}} \\ \\ \tan \frac{\alpha}{2} &= \pm \sqrt{\frac{1- \cos \alpha }{1+ \cos \alpha }} \\ \end{align}