If $\frac { 3 + i \sin \theta } { 4 - i \cos \theta } , \theta \in [ 0,2 \pi ]$, is a real number, then an argument of $\sin \theta + i \cos \theta$ is\\
(1) $\pi - \tan ^ { - 1 } \left( \frac { 4 } { 3 } \right)$\\
(2) $\pi - \tan ^ { - 1 } \left( \frac { 3 } { 4 } \right)$\\
(3) $- \tan ^ { - 1 } \left( \frac { 3 } { 4 } \right)$\\
(4) $\tan ^ { - 1 } \left( \frac { 4 } { 3 } \right)$