= Solution
Writing the square coordinates modulo one, the curve has the parametrization
$$
t\longmapsto(2t,3t)\pmod1.
$$
It is therefore the $(2,3)$ <torus knot>, or trefoil, on the common boundary of the two solid tori. Applying the <Seifert-van Kampen theorem> to the complements on the two sides gives one generator $a$ for the meridian of one solid torus and one generator $b$ for the other; the boundary slope identifies two turns of the first with three turns of the second. Hence
$$
\boxed{\pi_1(S-K)\cong\langle a,b\mid a^2=b^3\rangle.}
$$
This group is nonabelian: imposing the additional relation $a^2=b^3=1$ gives a quotient
$$
\langle a,b\mid a^2=b^3=1\rangle\cong C_2*C_3,
$$
which maps onto the nonabelian group $S_3$ by sending $a$ to a transposition and $b$ to a three-cycle. An abelian group cannot have a nonabelian quotient.
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