I would lay the flat sheet on the mattress and then, allowing about one inch "give" at each corner, I would pin straight down, mitering the corners. Then trim off the mitres and hem the bottom edges of the sheet and run elastic through the hem. Flat sheets are considerably wider and longer than a fitted sheet, so I would probably trim the sheet so that I had about 6" on each edge (past the depth of the mattress) to allow for the newly fitted sheet to fit nicely around the mattress.
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