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