Answer
$\frac{7\pi}{4}$
Work Step by Step
1. $sin\theta-cos\theta=-\sqrt 2 \Longrightarrow \frac{\sqrt 2}{2}sin\theta-\frac{\sqrt 2}{2}cos\theta=-1 \Longrightarrow cos\frac{\pi}{4}sin\theta-sin\frac{\pi}{4}cos\theta=-1 \Longrightarrow sin(\theta-\frac{\pi}{4})=-1$
2. $\theta-\frac{\pi}{4}=2k\pi+\frac{3\pi}{2}$
3. $\theta=2k\pi+\frac{7\pi}{4}$
4. Within $[0,2\pi)$, we have $\theta=\frac{7\pi}{4}$
