The integral \(\rm \displaystyle \int_0^\pi \sqrt{1+4 \sin ^2 \frac{x}{2}-4 \sin \frac{x}{2}} d x \) is equals 

1
π - 4 
2
\(\frac{2 \pi}{3}-4-4 \sqrt{3}\)
3
\(4 \sqrt{3}-4\)
4
\(4 \sqrt{3}-4-\frac{\pi}{3}\)

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