Find the integral of: \[ \displaystyle\int_{0}^{\pi} \sqrt{ 1+ 4\sin^{2}\frac{x}{2} - 4\sin\frac{x}{2}} \text{d}x \] If your answer is in the form \[ \text{a}\sqrt{3} - \text{b} - \frac{\pi}{\text{c}} \]. Find *a* + *b* + *c*.

This question is taken from JEE-Mains 2014.

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