Answer
$\theta=\frac{\pi}{4}+2k\pi$ and $\theta=\frac{3\pi}{4}+2k\pi$
Six example solutions for $k=0,\pm1:$
$-\frac{7\pi}{4}, -\frac{5\pi}{4}, \frac{\pi}{4}, \frac{3\pi}{4}, \frac{9\pi}{4}, \frac{11\pi}{4}$
Work Step by Step
Given $sin\theta=\frac{\sqrt 2}{2}$,
we can find two $\theta$ values in $[0,2\pi],$ $\theta=\frac{\pi}{4}, \frac{3\pi}{4},$
and the general solutions are $\theta=\frac{\pi}{4}+2k\pi$ and $\theta=\frac{3\pi}{4}+2k\pi$
where $k$ is any integer. Six example solutions for $k=0,\pm1:$
$-\frac{7\pi}{4}, -\frac{5\pi}{4}, \frac{\pi}{4}, \frac{3\pi}{4}, \frac{9\pi}{4}, \frac{11\pi}{4}$
