I went to the home improvement store, and I found I had a piece of plastic outside corner. I thought when I bought it several weeks ago, I was told it could be used for inside or outside corners.
They didn't have a drywall expert there, but one of the sales people had worked with drywall. He offered an option I would like to get comments on.
The store has paper tape with metal reinforcement bonded to it. The sales guy said to mud the joint, and apply this reinforced tape in the corner with the metal toward the wall. After that, treat it like regular paper tape.
Another customer said he thought the metal reinforced tape was weaker, because the mud couldn't bite into the metal like it could the paper tape. This guy, who wasn't a expert, said to use regular paper tape, then come back over it with a layer of fiberglass mesh tape. He said that would be the strongest way to repair that corner.