In this problem a modified Klein bottle (say $X$) is taken in account which is seen as embedded space in $\mathbb R^3$ (giving subspace topology on the usual self intersecting figure of Klein bottle in $\mathbb R^3$).
I have to prove its fundamental group is $\mathbb{Z}* \mathbb{Z}$. Secondly consider the space $Y$ by removing the open disc enclosed by the circle of self intersection of $X$. Find its fundamental group.
I even don't know how to proceed and apologize for the bad writing style.