Thanks guys - I managed to find some instructions on how to install the GP Thunder 8500 Angel eyes and I just tried this on my M3 Convertible.
I managed to install the passenger's side (right when viewed from the front) and this went fine.
However when I did the driver's side, the fitting just won't turn anti-clockwise to secure the bulb. This is after 2 hours of trying and applying plenty of pressure! I tried taking the fitting out of the electrical socket and trying the process all over again but still no luck - the fitting just wouldn't turn anti-clockwise.
So I put the stock/OEM fitting back in on both driver's and passenger's sides.
Has anyone got any suggestions for how I can get the driver's side to work?
Otherwise I will have to return the GP Thunder 8500 bulbs that I purchased from ElectronicWoot.
E93 M3 M-DCT JzB/Ext BB.