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The best way to make three-way mitre joints is to use a mitre saw and a Domino joiner. If you have tried the joint with a tablesaw and a shop-made routing jig, you know how slow and unreliable the method is.
You can cut the double mitres first, the Domino joiner will cut a mortise perpendicular to the mitre. The three pieces are assembled all at once.
Another approach is to cut the mortises first and then mitre the ends. Under this approach, the mortises are parallel to the stock. That means you can join any two pieces first and then add the third piece, making the assembly process easier.
The final clean-up is best done with a handplane:
You can cut the double mitres first, the Domino joiner will cut a mortise perpendicular to the mitre. The three pieces are assembled all at once.
Another approach is to cut the mortises first and then mitre the ends. Under this approach, the mortises are parallel to the stock. That means you can join any two pieces first and then add the third piece, making the assembly process easier.
The final clean-up is best done with a handplane: