Definition of Terms:

H = Height of rendered tile
dH = Height of rendered tile after tilt
L = Horizontal length of rendered tile
R = Ratio of full height vs tilted height
Tr = Theta rotation = Angle of rotation
Tt = Theta tilt = Angle of tilt
X = Number of horizontal pixels in original tile
Y = Number of vertical pixels in original tile
Orx = X Offset of tile to the right 
Ory = Y Offset of tile to the right
Odx = X Offset of tile below
Ody = Y Offset of tile below

Formulas:

dH = R * H
R = Cos(Tt)
H = Y*sin(90-Tr) + X*sin(Tr)
dH = Cos(Tt) * (Y*sin(90-Tr) + X*sin(Tr))

L = X*cos(Tr) + Y*cos(90-Tr)

Orx = X*cos(Tr)
Ory = Y*sin(Tr)

Odx = X*sin(Tr)
Ody = Y*cos(Tr)

Proofs would require me drawing pictures in Paint.  I will do so on request.