How can I caculate the density function of $\frac{(1-a^2)^2}{1-2a^2\cos(2 \beta \pi R)+a^4}$ with $R \sim N(\mu,\sigma^2)$?

Question

I have a gaussian distributed variable $R$ with a mean of $\mu$ and standard deviation of $\sigma$,the variance is the square of the standard deviation. The formula for the measurement uses $\frac{(1-a^2)^2}{1-2a^2\cos(2\beta \pi R)+a^4}$ in the calculation, where $R \sim N(\mu, \sigma^2)$ and the other parameters are constant in the formula. I need to know the density function that result from taking the formula $\frac{(1-a^2)^2}{1-2a^2\cos(2\beta \pi R)+a^4}$. How can I calculate that?