Let $Y_1 = S^1 \times D^2$, $Y_2 = S^1 \times D^2$ and $T_1,T_2 = S^1 \times S^1$. We consider $X=Y_1\cup Y_2 / $~ where ~ is $x \in T_1$ ~ $x \in T_2$.
I would like to find the fundamental group of X.
I see $X$ as two solid torus which have been gluing along their border. Am I right ? And so I think I should use the Van Kampen theorem but I don't really know how.
Thank you for your help !