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I've been using a cheap 3mm tap for some time now, after accidentally breaking a TiN-coated one. It has held up very well, despite not using oil. My thoughts are that if your breaking the tap, then your technique might need some revision. With 6061-T6 aluminum I tend to start with two turns and then back off one turn, and then do three turns, and back off one, then three more, etc. However, if the tap gets stuck, I will go turn it either way without applying too much force until it gets un-stuck.
Along with the 3mm tap I'm using a 2.5mm Tin-coated drill bit that I got from McMaster-Carr at least a year ago (again, I don't use oil, except when drilling through hardened steel).