Let's Integrate!-2

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.