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