# Finding the kernel of an epimorphism onto $S_3$?

Let $\Lambda$ denote the group with presentation $\langle a,b \mid abab^{-1}a^{-1}b^{-1}\rangle$. We define the following epimorphism from $\Lambda$ onto $S_3$:

$\theta: \Lambda(a,b) \rightarrow S_3$ using $a \mapsto (12)$ and $b \mapsto (23)$. We have $(12)(23)(23)^{-1}(12)^{-1}(23)^{-1}=e$ thus indicating that our homomorphism factors through the quotient modulo the normal subgroup $H$ of $F$ generated by $abab^{-1}a^{-1}b^{-1}$ and, by definition, $\Lambda=F/H$. Find an explicit, finite presentation for the kernel, $\kappa$, of the epimorphism

I know the kernel of $\theta$ is the set of all elements of $\Lambda$ that are mapped to $e\in S_3$ and is a normal subgroup of $\Lambda$. I'm a little new to finding kernels so I'm not sure how to proceed. What's a good way to find the kernel of this epimorphism?

$$\langle x,y,z \mid y^{-1}x^{-1}yzxz^{-1}, y^{-1}zxyx^{-1}z^{-1} \rangle,$$
where $x=a^2$, $y=b^2$, and $z=ab^2a^{-1}$.