Chapter 7 - Section 7.4 - Basic Trigonometric Equations - 7.4 Exercises - Page 569: 14

$\frac{\pi}{4}+k\pi$

$\tan \theta=1$ $\theta=\tan^{-1}1$ $\theta=\frac{\pi}{4}$ The only solution in the interval $(-\frac{\pi}{2}, \frac{\pi}{2})$ is $\theta=\frac{\pi}{4}$. Remember that tangent has period $\pi$, and we can add any multiple of $\pi$ to that solution and the original equation would still hold. So the solution is $\theta=\frac{\pi}{4}+k\pi$.