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Let \(S\) be the set of all real numbers \(x\) such that \(0 \le x \le 2016 \pi\) and \(\sin x < 3 \sin \frac{x}{3}\). The set \(S\) is the union of a finite number of disjoint intervals. Compute the total length of all these intervals.

 Apr 5, 2020
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The total length of the intervals is 168*pi.

 Apr 5, 2020

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