Sometimes I have been lucky and got broken taps out by using a hardened small punch made from a old tap or HSS (high speed steel)drill, hitting the tap to chip away pieces as it is holding on 3 points. As has been said a spark eroder is a good option but very expensive if you just walk into a engineering shop, Thay need to make a copper electrode ,setup the job and submerge the whole thing in dielectric fluid.just go with the leave it in and live with it.