I just can't seem to understand how to use G-B to solve the following problem...

Let M be the regular surface in R^3 given by

M = {(x,y,z) in R^3; 144(x^2+y^2) = (z^4-2z^2+2)^2, 0<z<2}.

Determine the value of the double integral of K over M, where K is the Gaussian curvature of M.