Answer
$\frac{7\pi}{4}$
Work Step by Step
Step 1. Rewrite the equation as $\frac{\sqrt 2}{2}sin\theta-\frac{\sqrt 2}{2}cos\theta=-1\longrightarrow cos(\frac{\pi}{4})sin\theta-sin(\frac{\pi}{4})cos\theta=-1\longrightarrow sin(\theta-\frac{\pi}{4})=-1$
Step 2. Solve the equation above to get $\theta-\frac{\pi}{4}=2k\pi+\frac{3\pi}{2}$. Thus $\theta=2k\pi+\frac{7\pi}{4}$
Step 3. Within $[0,2\pi)$, we have $\theta=\frac{7\pi}{4}$
