The Path of a Billiard Ball

A billiard ball starts from one corner of a equilateral triangular
pool table. The ball bounces 5 times and returns to the original corner.
Find the original angle of travel of the ball. [Let the initial corner
be located at the origin and the other corners be (10,0) and (5,5rt3).]

Repeat for 7 bounces.

For what initial angles will the ball end at the same corner
(and how many bounces)?

For what initial angles will the ball end at a different corner
(and how many bounces)?
Source: Many sources, submitted by Ravi Subramanian.
Solution
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