Fine sheaf and exact form

Question

I can't see why since $\xi$ is an element of $Z^2(U,\epsilon)$ and $\epsilon$ is fine, there exists a $\tau\in C^1(U,\epsilon)$ so that $\delta\tau=\xi$.

Answer 1

Fine sheaves have no higher cohomology, so any $k$-cocycle is a $k$-coboundary for $k\ge 1$.