Answer
There are 2 values of $x$ satisfying the equation $$x=\frac{3\pi}{4}$$ and $$x=\frac{7\pi}{4}$$
Work Step by Step
$$2\cot x+1=-1$$ $$2\cot x=-2$$ $$\cot x=-1$$
In the interval $[0,2\pi)$, there are 2 values of $x$ satisfying the equation, which is $$x=\frac{3\pi}{4}$$ and $$x=\frac{7\pi}{4}$$
