Answer
$ \frac{\pi}{6}, \frac{3\pi}{2}$
Work Step by Step
Step 1. Use the Half-Angle Formula $sin\frac{\theta}{2}=\sqrt {\frac{1-cos\theta}{2}}$ and take the square of both sides of the equation, we otbain $cos^2\theta-2sin\theta cos\theta+sin^2\theta=1-cos\theta$
Step 2. Use the Pythagorean Identity $cos^2\theta+sin^2\theta=1$, the above equation becomes
$1-2sin\theta cos\theta=1-cos\theta$ which gives $cos\theta(1-2sin\theta)=0$
Step 3. The solutions for the above equation are $cos\theta=0$ or $sin\theta=\frac{1}{2}$
Step 4. By limiting $\theta\in [0,2\pi)$, we get the possible answers as $\theta=\frac{\pi}{2},\frac{3\pi}{2}, \frac{\pi}{6}, \frac{5\pi}{5}$, plug them in the original equation and check signs, we can find only two final solutions $\theta=\frac{3\pi}{2}, \frac{\pi}{6}$
