By symmetry $E(\tfrac{X_1+X_2}2\mid T)=\bar X$, with variance $\theta(1-\theta)/n$

Let $X_1,X_2,\dots,X_n$ be a random sample of size $n$ from Bernoulli distribution with parameter $\theta$. Then variance of conditional expectation of $\bigl(\frac{X_1+X_2}2\bigr)$ given $\sum_{i=1}^nX_i$ is: