Answer
$\frac{3\pi}{2}$
Work Step by Step
Step 1. Given the equation $tan(\frac{x}{2})=-1$, we can find the solution in $[0,\pi)$ as $\frac{x}{2}=\frac{3\pi}{4}$ or $x=\frac{3\pi}{2}$
Step 2. Consider the original function has a period of $2\pi$; we can express all the solutions as $x=2k\pi+\frac{3\pi}{2}$ where $k$ is an integer. Thus, within $[0,2\pi)$, we have $x= \frac{3\pi}{2}$ as the solution to the original equation.
