Problem
2017 AMC 8 Problem 25
In the figure shown, \overline{US} and \overline{UT} are line segments each of length 2, and m\angle TUS = 60^\circ. Arcs \text{arc }TR and \text{arc }SR are each one-sixth of a circle with radius 2. What is the area of the region shown?
![[asy]draw((1,1.732)--(2,3.464)--(3,1.732)); draw(arc((0,0),(2,0),(1,1.732))); draw(arc((4,0),(3,1.732),(2,0))); label("$U$", (2,3.464), N); label("$S$", (1,1.732), W); label("$T$", (3,1.732), E); label("$R$", (2,0), S);[/asy]](/static/aops/79f3ffcfa12364f64959c7aeadc809ba8d2aa6ac.png)
\textbf{(A) }3\sqrt{3}-\pi\qquad\textbf{(B) }4\sqrt{3}-\frac{4\pi}{3}\qquad\textbf{(C) }2\sqrt{3}\qquad\textbf{(D) }4\sqrt{3}-\frac{2\pi}{3}\qquad\textbf{(E) }4+\frac{4\pi}{3}
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