In the figure shown, $\overline{US}$ and $\overline{UT}$ are line segments each of length 4, and $m\angle TUS=60^{\circ }$. Arcs $\stackrel{⌢}{\mathrm{TR}}$ and $\stackrel{⌢}{\mathrm{SR}}$ are each one-sixth of a circle with radius 4. What is the area of the region shown?