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Math Prize 2016 Problem 7

Source:

September 12, 2016
Math Prize for Girls

Problem Statement

Let SS be the set of all real numbers xx such that 0≤x≤2016π0 \le x \le 2016 \pi and sin⁡x<3sin⁡(x/3)\sin x < 3 \sin(x/3). The set SS is the union of a finite number of disjoint intervals. Compute the total length of all these intervals.
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