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