$\begin{array}{l}\text{A trianglular park has a pole centred on it such that the line joining its top and vertices include an angle}\\ \text{of }\frac{\pi }{3}.\text{\hspace{0.17em} If the circum radius of the triangle is 2 units, then the height of the pole is}\end{array}$

• A

  $\frac{1}{\sqrt{3}}$

• B

  $\frac{2\sqrt{3}}{3}$

• C

  $2\sqrt{3}$

• D

  $\sqrt{3}$