how I must prove that the fundamental group of this shape with base point which is heavily shaded is $\left \langle a^{2},b^{2},aba^{-1},bab^{-1} \right \rangle$,and I want to use van kampen theorem.very naturally I think to pick the eight figure each side of the base point and do the van kampen theorem but it didn't go well,it will be great if you help me with some hint or explanation.
Applying van Kampen to the open cover formed by small enough open neighborhoods around the two figure eight $\Large∞$ which meat at the heavily shaded dot $\bullet$, you see that $$π_0(\Large∞\hspace{-5pt}\small\bullet\hspace{-5pt}\Large∞, \small\bullet)\approx π_0(\Large∞\hspace{-3pt}\small\bullet,\bullet) *π_0(\small\bullet\hspace{-3pt}\Large∞,\small\bullet)$$ Now $π_0(\Large∞\hspace{-9pt}\small\bullet\hspace{6pt},\bullet)$ is generated by $a^2$ and $b$, and there is an isomorphism $$\beta_a:π_0(\Large∞\hspace{-9pt}\small\bullet\hspace{6pt},\bullet)\to π_0(\small\bullet\hspace{-3pt}\Large∞\small,\bullet)$$ given by sending the class of a loop $\gamma$ to the class of the loop $a\gamma a^{-1}$, which means that $π_0(\small\bullet\hspace{-3pt}\Large∞\small,\bullet)$ is generated by $a^2$ and $aba^{-1}$.