Find the Length of the Curve $y=2 \ln \left(\sin \frac{x}{2}\right), \frac{\pi}{5} \leq x \leq \pi$

Multiple Choice

Find the length of the curve. $y=2 \ln \left(\sin \frac{x}{2}\right) , \frac{\pi}{5} \leq x \leq \pi$

A) $\ln (2+\sqrt{5})$
B) $\ln (\sqrt{5})$
C) $\ln (5)$
D) $\ln (2 \sqrt{5})$
E) None of these