A coin strikes the circumference of a circle from within the boundary of the circle at some random angle.

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A coin strikes the circumference of a circle from within the boundary of the circle at some random angle theta normal to tangent at that point (where theta is a constant), and keeps moving in the same plane as if there is no friction. At which strike with circumference again (n = ?), coin repeats its trajectory/ path? (For theta = 0, 30, 45 degrees, etc., the solution is simple. But what if theta is not among these? )