Answer
$\{ -\frac{5\pi}{4}, -\frac{\pi}{4}, \frac{3\pi}{4}, \frac{7\pi}{4} \}$
Work Step by Step
Step 1. Rewrite the equation as $tan(x)+1=0$ and define a function $f(x)=tan(x)+1$.
Step 2. Graph the function in the interval of $[-2\pi,2\pi]$ as shown in the figure.
Step 3. Identify zeros as $x=-\frac{5\pi}{4}, -\frac{\pi}{4}, \frac{3\pi}{4}, \frac{7\pi}{4}$
Step 4. We conclude the solution set in $[-2\pi,2\pi]$ is $\{ -\frac{5\pi}{4}, -\frac{\pi}{4}, \frac{3\pi}{4}, \frac{7\pi}{4} \}$
