Here is an interesting problem, which I could not solve and would appreciate any comment in solving it;

Assume that we have omitted infinite lines from $\mathbb{C}P^2$ to obtain $\mathbb{C}^2$ and now, consider the following lines in which $(z,w)$ is the coordinate of $\mathbb{C}^2$: $z=0, z=1, w=0, w=1, z=w.$

What is the fundamental group of the complement of these lines in $\mathbb{C}^2$?