The integral $\int_{0}^{\pi} \sqrt{1+4 \sin ^{2} \frac{x}{2}-4 \sin \frac{x}{2}} d x$ equals :
$\pi-4$
$\frac{2 \pi}{3}-4-4 \sqrt{3}$
$4 \sqrt{3}-4$
$4 \sqrt{3}-4-\frac{\pi}{3}$
Correct Option: , 4
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