First two moments of $\sin(X_1)/\sin(X_2)$ where $X_1$ and $X_2$ are independent Gaussian random variables

Question

Let $X_1\sim\mathcal{N}(\mu_1,\sigma_1)$ and $X_2\sim\mathcal{N}(\mu_2,\sigma_2)$ be two independent random variables.

The task is to compute \begin{equation} E\left[\frac{\sin(X_1)}{\sin(X_2)}\right] = \;? \end{equation} and \begin{equation} E\left[\left(\frac{\sin(X_1)}{\sin(X_2)}\right)^2\right] = \;? \end{equation}