I've sharpened them freehand using the edge of a thin cut off disc. Works okay if you're careful.You sharpen countersinks by grinding this face. How much you grind depends on how far the cutting edge is rolled from using a blunt one. If it's badly worn you might have to grind a few mm, if it's only just blunt then it'll just need a lick.
The same applies to gear cutters, if you use a blunt one you'll quickly trash the entire cutter.
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