Answer
$\frac{\pi}{2},\frac{3\pi}{2},\frac{\pi}{4},\frac{5\pi}{4}$
Work Step by Step
Step 1. Rewrite the equation $1+cot^2\theta=cot\theta+1 \longrightarrow cot\theta(\theta-1)=0 $. Thus $cot\theta=0$ or $cot\theta=1$
Step 2. For $cot\theta=0$, we have $\theta=\frac{\pi}{2},\frac{3\pi}{2}$
Step 3. For $cot\theta=1$, we have $\theta=\frac{\pi}{4},\frac{5\pi}{4}$
