I have a finite étale morphism $f \colon Z \rightarrow X$ and I define the sheaf of set $\mathcal{F}_Z$ on $X_{\acute{e}tale}$ as: $$ \mathcal{F}_Z(U) = Hom_X(U,Z)$$ this is a locally constant sheaf. I want to prove that the pullback of this sheaf on $Z_{\acute{e}tale}$ is constant. So basically I want to prove that for any étale map $g \colon U \rightarrow Z$ the number of map $g' \colon U \rightarrow Z$ such that $g' \circ f = g \circ f$ is $deg(f)$.