A loss function engineered to make $\bar X$ both Bayes and minimax

Suppose $X_1,X_2,\dots,X_n$ be i.i.d. Bernoulli($\theta$). Let the loss function for the problem of estimation of $\theta$ be given by $L(\theta,a)=\dfrac{(\theta-a)^2}{\theta(1-\theta)}$. Let the pdf of the prior for $\theta$ ($\pi(\theta)$) be given by $\pi(\theta)=1,\ 0\le\theta\le1$. Let $\bar X$ be the sample mean. Then: