Consider the following $G = (\mathbb{C}^*)^{\times 3}$-action on $\mathbb{A}^6$:

$(\lambda_0,\lambda_1,\lambda_2) \cdot (x_0,x_1,x_2,y_0,y_1,y_2) = (\lambda_0x_0,\lambda_1x_1,\lambda_2x_2,\frac{\lambda_0^2}{ \lambda_1\lambda_2}y_0,\frac{\lambda_1^2}{ \lambda_0\lambda_2}y_1,\frac{\lambda_2^2}{\lambda_0\lambda_1}y_2)$.

I need some help determining the GIT quotient of $\mathbb{A}^6$ by $G$.

The union of zero-sets $Z = V(x_1,y_1) \cup V(x_2,y_2) \cup V(x_3,y_3) \cup V(x_1,x_2,x_3)$ in $\mathbb{A}^6$ appears to be the locus of non-stable points.

How does the resulting geometric quotient of $\mathbb{A}^6 \backslash Z$ by $G$ look like as an algebraic variety? How does one generally go about in determining such quotients after identifying the stable locus?