7.6 Exercise 94

Find the exact value.

Find $\sin \left(2 \theta\right) , \cos \left(2 \theta\right) ,$ and $\tan \left(2 \theta\right)$ given $\sec \theta = - \frac{5}{3}$ and $\theta$ is in the interval $\left[\frac{\pi}{2} , \pi\right] .$