The first step was to let $\displaystyle \displaystyle \begin{align*} u = \csc{x} + \tan^2{2x} \end{align*}$ so that $\displaystyle \displaystyle \begin{align*} f = \sin{u} \end{align*}$. Then $\displaystyle \displaystyle \begin{align*} \frac{df}{dx} = \frac{df}{du} \cdot \frac{du}{dx} \end{align*}$. Finding $\displaystyle \displaystyle \begin{align*} \frac{df}{du} \end{align*}$ is easy. In this case, $\displaystyle \displaystyle \begin{align*} \frac{du}{dx} \end{align*}$ is not so easy, you have to use the Chain Rule again. See how you go.