Practice: Finding the sum of several cosines

Geometry Level 3

What value of $N$ in the interval $[0, 90]$ satisfies the following equation: $\begin{aligned} \frac { \sin N ^ \circ } { 2 \sin 5 ^ \circ } - \frac {1}{2} = & \cos 10 ^ \circ + \cos 20 ^ \circ + \cos 30^ \circ + \cos 40 ^ \circ \\ &+ \cos 50 ^ \circ + \cos 60^ \circ + \cos 70 ^ \circ + \cos 80 ^ \circ\, ?\\ \end{aligned}$