Answer
$\{ 0.3649, 1.2059, 3.5065, 4.3475 \}$
Work Step by Step
Step 1. Let $u=tan(x)$; we can rewrite the equation as $u^2-3u+1=0$, which gives $u=\frac{3\pm\sqrt {5}}{2}$ or $u=0.3820$ and $u=2.6180$
Step 2. For $tan(x)=u=0.3820$, we can find the reference angle as $x_0=tan^{-1}(0.3820)\approx0.3649$
and all x-values in $[0,2\pi)$ as $x\approx0.3649$ and $x=\pi+x_0=3.5065$
Step 3. For $tan(x)=u=2.6180$, we can find the reference angle as $x_0=tan^{-1}(2.6180)\approx1.2059$,
and all x-values in $[0,2\pi)$ as $x\approx1.2059$ and $x=\pi+x_0\approx4.3475$
Step 4. The solutions for the original equation in $[0,2\pi)$ are $\{ 0.3649, 1.2059, 3.5065, 4.3475 \}$
