Solution
= Solution
Each $U_j$ is isomorphic to $\mathbb C$ and is therefore contractible. Every <complex line bundle> over a contractible paracompact space is trivial, so $L|_{U_0}$ and $L|_{U_1}$ admit the required trivializations.
= Solution
Each $U_j$ is isomorphic to $\mathbb C$ and is therefore contractible. Every <complex line bundle> over a contractible paracompact space is trivial, so $L|_{U_0}$ and $L|_{U_1}$ admit the required trivializations.