3D Rotation as a Projective Transformation

Question

I have a 8-parameter projective transformation, which maps a unit square into a quadrilateral on the plane (green).

Now, I want to "rotate the image by 120 degrees in 3D around the local Y axis" (red). So I need a 8-parameter projective transformation, which maps the unit square into that new quadrilateral.

I can create a 3D rotation matrix. My idea was to "turn it" into a projective transform, and combine with the previous transform, but how do I turn it into a projective transform?

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By a Projective Transformation, I mean a matrix M 3x3, bottom right value is 1. It maps from a plane to a plane this way:

Z    := (M[3,1]*x + M[3,2]*y + M[3,3]);
newX := (M[1,1]*x + M[1,2]*y + M[1,3]) / Z;
newY := (M[2,1]*x + M[2,2]*y + M[2,3]) / Z;