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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