Van's right, you'll be in for some JC/spackle filling and sanding here almost no matter what--- and there are a couple of geometry traps that would be easy to miss. The gap will be too wide for a clean-looking tape fix. It's also too wide for a 2x
wedge to
cover the whole distance--- and that solution doesn't
line the faces up correctly at the corners, really (though it's fudge-able).
Each
flat frame wants to be extended with a 3-1/8" deep
wedge ripped (out of 2x4?) at 22.5 degrees-- and then attached (square side against the frame) flush w/ the lauan
face so that it's just more "wall" there at the corner. It mmmmmight be better to err on the slightly too-small side and fill gaps, rather than be too big and have to keep re-ripping? (Depending on if you have to do this with the walls already in place).
Do your painter a favor and try to do as much of the cosmetic fill&sand as you can before handing it over to them. This isn't a happy fix for them, I suspect-!