Problem 7

Carlos was playing football on a square surrounded by apartment blocks, and two of these buildings were touching at their corners with their adjacent walls forming an acute angle. Carlos kicked the ball on the ground into the opening, in a direction parallel to one of the walls. After exactly 29 bounces, the ball rolled right back to Carlos from the exact same direction he kicked it. What is the angle between the two walls? Give your answer in radians rounded to 5 decimal places.