there's no need to tape inside ceiling corners for existing skimmed boards - you simply trowel into the corner the depth of your skim coats - you dont need to turn down the wall.
going over previously skimmed work, & given you mention a "painted" ceiling - then you pre-wash the painted ceiling with two coats of 50:50 Pva and water, & go at it when the second coat is tacky.
if you want to know a little more about how to do inside ceiling corners then come back?
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