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JEE Advanced 2016 Paper 1 Mathematics Question 39

Let \(S = \displaystyle\{ x \in (-\pi, \pi) : x \neq 0, \pm \frac{\pi}{2}\}\). The sum of all distinct solutions of the equation \(\sqrt{3} \text{sec} x + \text{cosec}{x} + 2 (\text{tan}x - \text{cot}x) = 0\) in the set \(S\) is equal to

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