Mean Point

$n$ independent points $P_i = (X_i,Y_i)$ are selected uniformly at random from the boundary of the unit circle. Define $\overline{X} = \displaystyle \dfrac{1}{n}\sum_{i=1}^n X_i$ and $\overline{Y} = \displaystyle \dfrac{1}{n}\sum_{i=1}^n Y_i$. Compute $\cov{\overline{X}}{\overline{Y}}$ when $n = 10$.