[Chris Itin]

Can you offer a more detailed explanation, Herb? I think I understand but seriously doubt it! More pieces and smaller angles? (A drawing would be helpful...)

Maybe this will help.
When you make a normal 90-degree miter, you cut the pieces at 45 degrees (half of 90).
For this application, you are making angles of 45 degrees, so the cuts would be 22.5 degrees (half of 45).
That will make the mating pieces the same thickness.