How to prove that there are $O(T\ln T)$ zeros in the critical strip of the Riemann zeta function?

Question

Define $F(T)$ as the number of solutions to $\zeta(a+ ti) =0$ for $0\le t\le T$ and $0<a<1$.

How to show that $F(T)= O(T\ln T)$?

For clarity, $\zeta$ is the Riemann zeta function, $i$ is the imaginary unit and $O$ is big-O notation.