In the figure shown, US and UT are line segments each of length 2, and m∠TUS=60∘. Arcs \overarc{TR} and \overarc{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]
<spanclass=′latex−bold′>(A)</span>33−π<spanclass=′latex−bold′>(B)</span>43−34π<spanclass=′latex−bold′>(C)</span>23<spanclass=′latex−bold′>(D)</span>43−32π<spanclass=′latex−bold′>(E)</span>4+34π