## How to prove the UMVUE under these conditions

Hi everyone, the question is

Let $\mathbb{U}$ be the set of all unbiased estimators of 0. Namely,

$\mathbb{U}$={ $U(X): E_{\theta}(U(X)) = 0,$ for all $\theta$ $\Omega$}.
Then prove $\delta(X)$ is an UMVUE of $\theta$ iff for any $U(X)$ $\mathbb{U}$, $Cov_{\theta}(\delta(X),(U(X)) = 0$.
, and give a geometrical interpretation.
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I only figured that $E_{\theta}(U(X)\delta(X))=0$ so far, and I have no idea if I can use Lemann-Scheffe theorem to prove.