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.
The total length of the intervals is 168*pi.
+170 
