Answer
$0.285,3.427$
Work Step by Step
1. $sin(\theta+1)= cos\theta\Longrightarrow sin\theta cos1+cos\theta sin1-cos\theta=0\Longrightarrow tan(\theta)=\frac{1-sin1}{cos1}$
2. For $tan(\theta)=\frac{1-sin1}{cos1}\approx0.2934$, we have $\theta\approx k\pi+0.285$
3. Within $[0,2\pi)$, we have $\theta=0.285,3.427$
