Answer
$\{1.2971, 2.6299,4.4387, 5.7715 \}$
Work Step by Step
Step 1. Letting $u=tan(x)$, we have $u^2-3u-2=0$ thus $u=\frac{3\pm\sqrt {17}}{2}$
Step 2. For $tan(x)=u=\frac{3+\sqrt {17}}{2}\approx3.5616$, we have the reference angle $x_0=tan^{-1}(3.5616)\approx1.2971$ with solutions $x_1=x_0=1.2971$, $x_2=\pi+x_0\approx4.4387$
Step 3. For $tan(x)=u=\frac{3-\sqrt {17}}{2}\approx-0.5616$, we have the reference angle $x'_0=tan^{-1}(0.5616)\approx0.5117$ with solutions $x_3=\pi-x'_0\approx2.6299$, $x_4=2\pi-x'_0\approx5.7715$
Step 4. We have the solution set as $\{1.2971, 2.6299,4.4387, 5.7715 \}$
