Answer
$\{\frac{\pi}{4}, 2.0344, \frac{5\pi}{4}, 5.1761 \}$
Work Step by Step
Step 1. Rewrite the equation as $tan(x)+1+tan^2(x)=3$; we have $tan^2(x)+tan(x)-2=0$
Step 2. Let $u=tan(x)$; we have $u^2+u-2=0$ or $(u+2)(u-1)=0$
Step 3. For $tan(x)=u=1$, we have $x=\frac{\pi}{4}, \frac{5\pi}{4}$
Step 4. For $tan(x)=u=-2$, we have the reference $x_0=tan^{-1}2\approx1.1071$ and the solutions $x_1=\pi-x_0\approx2.0344$, $x_2=2\pi-x_0\approx5.1761$
Step 5. We have the solution set as $\{\frac{\pi}{4}, 2.0344, \frac{5\pi}{4}, 5.1761 \}$
