Suppose $[X\mid \theta]\sim\operatorname{Uniform}([0, \theta])$ and $B$ is is a beta distributed random variable. Additionally, $\max(X\_1,…,X\_n)/θ\sim \operatorname{Beta}(n+1,1)$

Show that $\hat{θ}= \frac{n+2}{n+1} \max(X\_1,…,X\_n)$ and find the variance of $\hat\theta$ given $\theta$.

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I found: $E[B]= \frac{n+1}{n+2}$ and $V[B]= \frac{n+1}{(n+2)^2(n+3)}$

How do I find the variance of $\hat{\theta}\mid \theta?$