Chapter 7 - Section 7.4 - Basic Trigonometric Equations - 7.4 Exercises - Page 569: 32

$\frac{3\pi}{4}+k\pi$

$\cot\theta+1=0$ $\cot\theta=-1$ $\tan\theta=\frac{1}{-1}$ $\tan \theta=-1$ $\theta=\dots$, $-\frac{\pi}{4}$, $\frac{3\pi}{4}$, $\frac{7\pi}{4}$, $\frac{11\pi}{4}$, $\dots$ So $\theta=\frac{3\pi}{4}+2k\pi$.