\\
& + & (2(z^1)^2 z^4 + 2 (z^2)^2 z^4 + 2 (z^3)^2 z^4 - (z^4)^3 - z^4 (z^5)^2
- z^4 (z^6)^2 - z^4 (z^7)^2  \nonumber \\
&& - 2\sqrt{3} z^3 z^4 z^8 - 2\sqrt{3} z^1 z^6 z^8 + 2\sqrt{3} z^2 z^7 z^8)%
{\rm d}z^4  \label{SU3-2} \\
& + & (2(z^1)^2 z^5 + 2 (z^2)^2 z^5 + 2 (z^3)^2 z^5 - (z^4)^2 z^5 - (z^5)^3
- z^5 (z^6)^2 - z^5 (z^7)^2  \nonumber \\
&& - 2\sqrt{3} z^3 z^5 z^8 - 2\sqrt{3} z^2 z^6 z^8 - 2 \sqrt{3} z^1 z^7 z^8)%
{\rm d}z^5  \nonumber \\
& + & (2(z^1)^2 z^6 + 2(z^2)^2 z^6 + 2(z^3)^2 z^6 - (z^4)^2 z^6 - (z^5)^2
z^6 - (z^6)^3 - z^6 (z^7)^2  \nonumber \\
&& - 2\sqrt{3} z^1 z^4 z^8 - 2\sqrt{3} z^2 z^5 z^8 + 2\sqrt{3} z^3 z^6 z^8)%
{\rm d}z^6  \nonumber \\
& + & (2(z^1)^2 z^7 + 2 (z^2)^2 z^7 + 2 (z^3)^2 z^7 - (z^4)^2 z^7 - (z^5)^2
z^7 - (z^6)^2 z^7 - (z^7)^3  \nonumber \\
&& + 2\sqrt{3} z^8(z^2 z^4 - z^1 z^5 + z^3 z^7){\rm d}z^7] = 0 \, , 
\nonumber\end{aligned}$$ where

$$\begin{aligned}
\Delta & = & 2 (z^1)^2 z^7 + 2 (z^2)^2 z^7 + 2 (z^3)^2 z^7 - (z^4)^2 