Answer
$\frac{\pi}{2},\pi$
Work Step by Step
1. $sin(\theta)-cos(\theta)=1 \Longrightarrow (sin(\theta)-cos(\theta))^2=1 \Longrightarrow 1-2sin(\theta)cos(\theta)=1\Longrightarrow sin(2\theta)=0 $,
2. For $ sin(2\theta)=0$, we have $2\theta=k\pi$ or $\theta=\frac{k\pi}{2}$
3. Within $[0,2\pi)$, we have $\theta=0,\frac{\pi}{2},\pi,\frac{\pi}{2}$, check only $\theta=\frac{\pi}{2},\pi$ fit the original.
