JEE Math Practice Question

If $${{3 + i\sin \theta } \over {4 - i\cos \theta }}$$, $$\theta $$ $$ \in $$ [0, 2$$\theta $$], is a real number, then an argument of sin$$\theta $$ + icos$$\theta $$ is :

1. A.$$\pi - {\tan ^{ - 1}}\left( {{3 \over 4}} \right)$$
2. B.$$ - {\tan ^{ - 1}}\left( {{3 \over 4}} \right)$$
3. C.$${\tan ^{ - 1}}\left( {{4 \over 3}} \right)$$
4. D.$$\pi - {\tan ^{ - 1}}\left( {{4 \over 3}} \right)$$