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Hi LoriLori. I've had bad luck with painter's tape, too. I don't use it to do anything but mask hardware now. Your best bet is to clean up those edges with the lighter color first, and then go in by hand and eyeball a straight line... you should have a good guide at this point since you already painted with tape and if you use a good brush and have a steady hand it should even out nicely.
I don't know about the other sort of tape - it might be worth buying a roll and giving it a try in one area. I think you're going to be best off by doing it without tape at all, though.
The best way to clean up and straighten that edge is: for latex paint / mineral spirits on a rag using a painters 5in1 tool to get into the corner. If it is oil based paint use laquer thinner.