Answer
$\{\frac{\pi}{4}, 2.5536, \frac{5\pi}{4}, 5.6952 \}$
Work Step by Step
Step 1. Factor the equation as
$(3tan(x)+2)(tan(x)-1)=0$, thus $tan(x)=1$ and $tan(x)=-\frac{2}{3}$
Step 2. For $tan(x)=1$, we can find all x-values in $[0,2\pi)$ as $x=\frac{\pi}{4},\frac{5\pi}{4}$
Step 3. For $tan(x)=-\frac{2}{3}$, we can find the reference angle as $x_0=tan^{-1}(\frac{2}{3})\approx0.5880$ and all x-values in $[0,2\pi)$ as $x=\pi-x_0\approx2.5536$ and $x=2\pi-x_0\approx5.6952$
Step 4. The solutions for the original equation in $[0,2\pi)$ are $\{\frac{\pi}{4}, 2.5536, \frac{5\pi}{4}, 5.6952 \}$
