Let $X$ be a locally connected space a sheaf $F$ on $X$ is called locally constant whenever each $x\in X$ has a basis of open neighbourhoods$N_x$ and if $U,V \in N_x$ such that $U$ is a subset of $V$ then the restriction map $FV\rightarrow FU$ is a bijection.
How can I show that the sheaf $F$ is locally constant iff the associated etale space over $X$ is a covering?