final great circle to draw triange group (2,3,4)

Question

I have all the great circles to draw the triangle group (2,3,4) except for one. I'm missing the great circle that would intersect (1) the intersection of the green and violet arcs and (2) the intersection of the blue and cyan (and black) arcs. The instruction in the first curly brackets is the "tilt angle" and the instruction in the second curly brackets is the "rotation angle." But when trying to input the appropriate angles, my output is nonsense.

\documentclass{amsart}
\usepackage{blochsphere}
\pgfsetlayers{back,main,front}

\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\usepgfplotslibrary{fillbetween}


\begin{document}

\begin{tikzpicture}
    \begin{blochsphere}[radius=3cm, tilt=5, rotation=-40, nested=true]
        \drawBall

            % {tilt angle}{rotation angle}
        \drawBallGrid[style={draw}]{360}{90}

        \drawGreatCircle[style=red]{45}{-90}
        \drawGreatCircle[style=cyan]{-45}{-90}
        \drawGreatCircle[style=green]{60}{-35}
        \drawGreatCircle[style=yellow]{-60}{35}
        \drawGreatCircle[style=blue]{-60}{-35}
        \drawGreatCircle[style=violet]{90}{90}
    \end{blochsphere}
    
\end{tikzpicture}

\end{document}