Three random variables $X_1, X_2, X_3$ are drawn from a population with mean $\mu$ and variance $\sigma^2$. However, they are not independent: the covariance between any pair is $Cov(X_i, X_j) = \rho\sigma^2$ for $i \neq j$. If we calculate the standard sample variance $s^2 = \frac{1}{2} \sum_{i=1}^3 (X_i - \bar{X})^2$, what is its expected value $E[s^2]$?