Question: How do I set up coordinates system for general relativity besides the usual ones, cartesian, cylindrical, spherical, etc?

How can I resolve the following error message? More specifically, how do I set up a coordinate system different from cartesian, spherical, etc in order to pass it to the metric? 

restart;
with(Physics);

Setup(mathematicalnotation = true);
                 [mathematicalnotation = true]
Setup(signature = `+---`);
                     [signature = + - - -]

ds2 := [(x^2-y^2)*cos(2*u)+2*x*y*sin(2*u)]*(du^2)-2*x*(dv^2)-dx^2-dy^2;
Setup(coordinates = (Z = [u, v, x, y], metric = ds2));
* Partial match of  'coordinates' against keyword 'coordinatesys\

  tems'
Error, (in Physics:-Setup) expected a list with 4 names, where 4 is the spacetime dimension, or one of the keywords cartesian, spherical, cylindrical; received: ds2