Etale locally free sheaf is always locally free in Zariski topology.

Question

I'm trying to solve exercise III.10.5 from Hartshorne "Algebraic geometry". Let $\mathcal F$ be a coherent sheaf on a scheme $X$ locally free in 'etale topology', namely for any $x \in X$ there is an 'etale' map $f: U \to X$, together with a point $x' \in U$, $f(x')=x$, such that $f^* \mathcal F $ is a free $\mathcal O_U$ module, then $\mathcal F$ is locally free.