Create a Frame, wait for it to be properly shown and print its insets obtained from getInsets(). On various platforms they are different but on Unity in Ubuntu 15.10 they are just empty, all zeros. (Unlike e.g. Xfce4 of Ubuntu 14.04)

getLocation() of the Frame returns, in this case, the coordinates of the client area.
Perhaps getLocationOnScreen() works better but we have this API, and it should work.