Answer
$$ - \cos \left( {\sin \theta } \right) + C$$
Work Step by Step
$$\eqalign{
& \int {\left[ {\sin \left( {\sin \theta } \right)} \right]} \cos \theta d\theta \cr
& {\text{substitute }}u = \sin \theta ,{\text{ }}du = \cos xdx \cr
& \int {\left[ {\sin \left( {\sin \theta } \right)} \right]} \cos \theta d\theta = \int {\sin u} du \cr
& {\text{find antiderivative }} \cr
& = - \cos u + C \cr
& {\text{write in terms of }}x,{\text{ replace }}u = \sin \theta \cr
& = - \cos \left( {\sin \theta } \right) + C \cr} $$
