Combining a lower and upper confidence limit into a two-sided interval

Let $T_1$ be a $100\cdot\alpha\%$ lower confidence limit for $\theta$ and $T_2$ be a $100\cdot\alpha\%$ upper confidence limit for $\theta$. Let $P[T_1<T_2]=1$ and $\tfrac12<\alpha<1$. Then a $100(2\alpha-1)\%$ confidence limit for $\theta$ is: