What's the conduction angle for a full wave rectifier with filter capacitor?
First, that equation is an approximation, based on x^2/2 being approximately equal to 1 - cos(x). It also assumes that the conduction angle is small compared to a cycle. For any reasonable conduction angle, these approximations are fairly accurate. Or, for ripple of about 15% or less it is reasonably accurate.

It is approximately valid for either full or half wave rectifiers. But, of course, everything else being equal, when you go from a full to half wave the ripple will double therefore the conduction angle will be the square root of 2 greater.