AMC 10 2020b Problem 14

As shown in the figure below, six semicircles lie in the interior of a regular hexagon with side length 2 so that the diameters of the semicircles coincide with the sides of the hexagon. What is the area of the shaded region ---- inside the hexagon but outside all of the semicircles? $\textbf{(A) } 6\sqrt3 - 3\pi \textbf{(B) } \frac{9\sqrt3}{2} - 2\pi \textbf{(C) } \frac{3\sqrt3}{2} - \frac{3\pi}{3} \textbf{(D) } 3\sqrt3 - \pi \textbf{(E) } \frac{9\sqrt3}{2} - \pi$