Combining two noisy estimates optimally

Two independent research groups each produce an unbiased estimate of the same fair value $\theta$: group one gives $T_1$ with variance $v_1$, group two gives $T_2$ with variance $v_2$. You will combine them linearly as $T = wT_1 + (1-w)T_2$.

What weight $w$ minimizes the variance of $T$, and what is the resulting variance? Evaluate for $v_1 = 4$, $v_2 = 1$.