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**Which integrals represent the area of the $\blue{\text{shaded region}}$ of the circle $\red{r=2\sin\theta}$?**
$I.\quad\displaystyle \int_{\tfrac{\pi}{3}}^{\tfrac{2\pi}{3}}{2 \sin^2\theta\,d\theta }$
$II.\quad\displaystyle \int_{\tfrac{\pi}{3}}^{\tfrac{\pi}{2}}{4 \sin^2\theta\,d\theta }$
$III.\quad\displaystyle \int_{\tfrac{4\pi}{3}}^{\tfrac{5\pi}{3}}{2 \sin^2\theta\,d\theta }$
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