axonometric projection transformations

High School and College were so long ago and I can't for the life of me figure this out (plus it doesn't help I was a music major):

Given a 3D point in space (x, y, z) and an angle of projection ϴ I want to convert to screen coordinates (x', y'). I can do this successfully going from space to screen via the following transformations:

x' = (x - y) * cos ϴ;
y' = (x + y) * sin ϴ - z;

I cannot however figure out the transformations for going from screen back to space assuming space.z = 0 after the transformation. Any help is much appreciated.

And if you are still interested in this kind of thing after this one is solved, I have a bunch more.

Thank you.

Ok I figured out one of them for a 2:1 isometric ratio.

space to screen:
x' = x - y
y' = (x + y) / 2 - z

screen to space (assuming z = 0):
x = x' / 2 + y' + z'
y = y' - x' / 2 + z'
z = z'