Linear Transformations · Challenge problem

For $k = 1, 2, \ldots, 8$ let $F_k$ be the reflection of the plane across the line through the origin making angle $15k^\circ$ with the positive $x$-axis. The composite $F_8\circ F_7\circ\cdots\circ F_2\circ F_1$ (apply $F_1$ first) is a rotation. Through how many degrees counterclockwise does it rotate? (Give an angle in $[0,360)$.)