How to project a 3D point on a plane into a 2D coordinate system

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When searching for 3D-projection you can find these diagrams, where the camera screens are always orthagonal to the x/y-axis. enter image description here

But how do you calculate the 2D-coordinates when you have a rotation of the screen like so:

enter image description here

In this example all the coordinates (x,y,z) of the points C,A,M and B are given as well as (if needed) the equation of the camera screen