Answer
$\frac{\pi}{4}$
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 $\theta+\frac{\pi}{4}=2k\pi+\frac{\pi}{2}$. Thus $\theta=2k\pi+\frac{\pi}{4}$
Step 3. Within $[0,2\pi)$, we have $\theta=\frac{\pi}{4}$
