Answer
$\frac{\pi}{2},\pi$
Work Step by Step
Step 1. $(sin(\theta)-cos(\theta))^2=1 \longrightarrow 1-sin(2\theta)=1$.
Thus $sin(2\theta)=0$
Step 2. For $sin(2\theta)=0$, we have $2\theta=k\pi$ and $\theta=\frac{k\pi}{2}$
Step 3. Within $[0,2\pi)$, find and check answers to get $\theta=\frac{\pi}{2},\pi$
