ILL 1974 Problem 37

Let $a, b$ , and $c$ denote the three sides of a billiard table in the shape of an equilateral triangle. A ball is placed at the midpoint of side $a$ and then propelled toward side $b$ with direction defined by the angle $\theta$ . For what values of $\theta$ will the ball strike the sides $b, c, a$ in that order?