Answer
$$ \sin \frac{\theta }{2} =\sqrt{\frac{1}{2} \left( 1-\cos \theta \right)}$$
Work Step by Step
Since
\begin{align*}
\sin^2\frac{\theta }{2}&= \frac{2\sin^2\frac{\theta }{2}}{2}\\
&= \frac{ \sin^2\frac{\theta }{2}+\sin^2\frac{\theta }{2}}{2}\\
&= \frac{1- \cos^2\frac{\theta }{2}+\sin^2\frac{\theta }{2}}{2}\\
&=\frac{1}{2} \left( 1-\cos \theta \right)
\end{align*}
Then
$$ \sin \frac{\theta }{2} =\sqrt{\frac{1}{2} \left( 1-\cos \theta \right)}$$
