You don't need the socket and the one listed in that article is incorrect. The more difficult task is removing the 3 phillips screws that keep that nut from spinning. Take the correct size phillip screwdriver and then strike with a hammer will make them come out easily without stripping the heads which is common.


The round 'nut' has a number of holes in it for tightening/alignment and if you put the edge of a screwdriver in one and tap lightly with a hammer it will loosen easily. .