A sheaf is called fine if basically it has partition of unit for endomorphisms. That is, if $P:E \rightarrow M$ is a sheaf, then $P$ is called fine if for for every locally finite open cover $\{U_{i}\}_{i \in I}$, with $U_{i} \subsetneq M$, $\bigcup\limits_{i \in I} U_{i} = M$ there exists sheaf endomorphisms $\psi_{i} :M \rightarrow M$ such that $Support(\psi_i) \subseteq U_{i}$ and $\Sigma_{i} \psi_i = 1$
The trivial sheaf is the function
\begin{gather*}P:M\times T \rightarrow M \\ (m,t)\rightarrow\ m \end{gather*}
with $M$ a topological space, $T$ an $A$-module with the discrete topology and the space étale $M \times T$ with the product topology.
I was wondering if the trivial sheaf is fine, in all cases, in some cases or what suffices so that it's fine.