Answer
$\theta=k\pi+\frac{\pi}{2}$ or $\theta=180^\circ k+90^\circ$ where $k$ is an integer.
Work Step by Step
1. Use the identity $cos(2\theta)=1-2sin^2\theta$, we have $sin^2\theta=-1+2sin^2\theta\longrightarrow sin^2\theta=1 \longrightarrow sin\theta=\pm1$
2. The period is $2\pi$ and the fundamental solutions (reference angles) in $[0,2\pi)$ are $\theta=\frac{\pi}{2},\pi+\frac{\pi}{2}$, thus the general solutions are $\theta=k\pi+\frac{\pi}{2}$ where $k$ is an integer.
3. We can also write the solutions as $\theta=180^\circ k+90^\circ$ where $k$ is an integer.
