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