Answer
$\boxed{\theta = \frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4}}$
Work Step by Step
$cos^2(\theta) = \frac{1}{2}$, which means $cos(\theta) = +\frac{\sqrt{2}}{2}$ or $cos(\theta) = -\frac{\sqrt{2}}{2}$
For the first case, $cos(\theta) = +\frac{\sqrt{2}}{2}$, $\theta = \frac{\pi}{4}, \frac{7\pi}{4}$.
For the second case, $cos(\theta) = -\frac{\sqrt{2}}{2}$, $\theta = \frac{3\pi}{4}, \frac{5\pi}{4}$.
Overall, the solutions for $\theta$ are: $\frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4}$.
