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