Chapter 7 - Section 7.4 - Basic Trigonometric Equations - 7.4 Exercises - Page 569: 16

$-0.32+k\pi$

$\tan \theta=-\frac{1}{3}$ $\theta=\tan^{-1}-\frac{1}{3}$ $\theta=-0.32$ The only solution in the interval $(-\frac{\pi}{2}, \frac{\pi}{2})$ is $\theta=-0.32$. 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 $\theta=-0.32+k\pi$.