Answer
$\boxed{\theta = \frac{\pi}{8}, \frac{3\pi}{8}, \frac{5\pi}{8}, \frac{7\pi}{8}}$
Work Step by Step
$tan^2(2\theta) =1$
$tan(2\theta) = +1$ or $tan(2\theta) = -1$
For the first case, $tan(2\theta) = +1$, $2\theta = \frac{\pi}{4}, \frac{5\pi}{4}$. This means that $\theta = \frac{\pi}{8}, \frac{5\pi}{8}$.
For the second case, $tan(2\theta) = -1$, $2\theta = \frac{3\pi}{4}, \frac{7\pi}{4}$.
This means that $\theta = \frac{3\pi}{8}, \frac{7\pi}{8}$.
Overall, the solutions for $\theta$ are: $\frac{\pi}{8}, \frac{3\pi}{8}, \frac{5\pi}{8}, \frac{7\pi}{8}$.
