1999 AIME Problem 11

Given that \sum_{k=1}^{35}\sin 5k=\tan \frac mn, where angles are measured in degrees, and m_{} and n_{} are relatively prime positive integers that satisfy \frac mn<90, 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.