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Let's Play Billiards!

Source: 1981 National High School Mathematics League, Problem 11

February 20, 2020

Problem Statement

A billiards table is in the figure of regular hexagon ABCDEFABCDEF. PP is the midpoint of ABAB. We shut the ball at PP, then it touches QQ on side BCBC, then it touches side CD,DE,EF,FACD,DE,EF,FA. Finally, the ball touches side ABAB again. Let θ=∠BPQ\theta=\angle BPQ, find the value range of θ\theta.
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