Minimum Variance Unbiased Estimator

We have a r.v. $\displaystyle X$~$\displaystyle Bin (12,\theta)$

And I have worked out that the Cramer Rao Lower Bound for the var of any unbiased est of $\displaystyle \theta$ to be

$\displaystyle \frac{1}{\frac{1}{12}(\frac{1}{\theta} + \frac{1}{1-\theta})}$

Now, I'm given that $\displaystyle T = \frac{\sum X_{i}}{12n}$

(in case there's any confusion, the sum is from i=1 to n, I'm not sure how to do that on LaTex)

How do I show that $\displaystyle T$ is a minimum variance unbiased estimator of $\displaystyle \theta$?