Understanding Seifert Van Kampen

I want to understand why $i_{1ast}(h)=i_{2ast}(h)$ is $1=alphabetaalpha^{-1}beta^{-1}.$

$i_{1ast}:pi_{1}(U_1cap U_2,x)rightarrowpi_1(U_1, x)$. Since $pi_{1}(U_1, x)={1}$ we must have $i_{1ast}$ as a trivial map. But I don’t understand what $i_{2ast}$ should be. It’s a map from $mathbb{Z}$ to $mathbb{Z}timesmathbb{Z}$. How can I identify $i_{2ast}$ and conclude $1=alphabetaalpha^{-1}beta^{-1}$?

The screenshot is from Mathonline Seifert Van Kampen Theorem Example 3 page.