Hi, recently I encountered a question concerning delta function as follows:

1/(r^2 times sin(theta)) times delta(r-r') times delta(theta-theta') times delta(phi-phi') in spherical coordinates. Now I'd like to make a little modification into 1/(r^2) times delta(r-r') times delta(cos(theta)-cos(theta')) times delta(phi-phi'). Does anyone tell me how to do that litte conversion, though may look easy at first sight?? Thank you very much!!

Please refer to this websites of spherical coordinates if necessary, thanks.

Dirac delta function - Mathematics wiki