2015 AIME I Problem 13

With all angles measured in degrees, the product \prod_{k=1}^{45} \csc^2(2k-1)^\circ=m^n, where m and n are integers greater than 1. Find m+n.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.