\textbf{111.} Assume $\sin\alpha = \dfrac{-3}{5}$ and the terminal side of arc $\alpha$ is in the third quadrant. What is the value of $\cos(\tan^{-1}(\sin 2\alpha))$?
$$\frac{25}{\sqrt{1201}} \quad (1) \qquad \frac{-25}{\sqrt{1201}} \quad (2) \qquad \frac{5}{\sqrt{51}} \quad (3) \qquad \frac{-5}{\sqrt{51}} \quad (4)$$