VTRMC 2013 Problem 1

Let $I=3\sqrt2\int^x_0\frac{\sqrt{1+\cos t}}{17-8\cos t}dt$ . If $0<x<\pi$ and $\tan I=\frac2{\sqrt3}$ , what is $x$ ?

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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