Answer:
Let \[\theta \] denote the angle at instant t. \[\frac{d\theta }{dt}=2\frac{d}{dt}(sin\theta )\] [given] \[\Rightarrow \] \[\frac{d\theta }{dt}=2\cos \theta \left( \frac{d\theta }{dt} \right)\] \[\Rightarrow \] \[1=2\cos \theta \] \[\Rightarrow \] \[2\cos \theta =1\] \[\Rightarrow \] \[\cos \theta =\frac{1}{2}\] \[\Rightarrow \] \[\theta ={{\cos }^{-1}}\left( \frac{1}{2} \right)=\frac{\pi }{3}.\] Hence, the required angles is \[\frac{\pi }{3}.\]
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