Broken tiny tap in aluminium

[Highpower]

I know I'm late to the party but I asked my dentist to save used dental burrs for me for this kind of thing with small taps or screws. The burrs aren't as sharp as they need to be anymore for working on teeth, but still good enough for grinding away metal.

They throw a mixture of slightly worn carbide and diamond burrs in an envelope (after they sterilize them) and give them to me when I go in for my cleanings. Gotta love a dentist that gives you free tools!

Try asking yours. Worst that could happen is they say no.