Advanced Excel Cartesian-Polar Angle Converter

i have a laserpoint on 2 stepper motors. with these, the laser can point in any direction. The laser unit can be placed anywhere in any direction.
Now the user points the laser to 3 different point and tells the system the x and y coordinates in the desired user defined coordinate system. This process is to teach the system the tranformation matrix. once this teaching is done, the user can command the laser to any point on the table, like x=6 and y=-3.5. The laser then point to this coordinates.

What i need now is an excel spreadsheet which shows me how to calculate something like that. As an input i put in the 3 points with x and y coordinates as well as the angles alpha and beta.
The excel then calculates the matrix.
in another Tab, i can put in then specific coordinates like the example above with x=6 and y=-3.5 and the excel uses the matrix to give out the calculated angles for alpha and beta.