Apply wood glue to the back of the piece and tack it in place as shown with a pneumatic brad gun and 18 gauge brads.
Building a hidden door in drywall.
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The miter faces the gap.
The drywall needs to be as thick as the original drywall on the wall.
That leaves a smooth wall so whatever you put in front of the opening will sit tightly against it.
First remove all the trim boards if any from around the door to the space you want for your secret room.
Done properly there should only be a small outline of the door with a 1 2 inch missing from the bottom.
Select the plywood waste and cut a piece 2 x the length of the door panel for the door extension brace select the 2 brace.
Using glue and 1 1 4 screws counter sink the screws attach the brace to the back side of the door panel 6 from the pivot edge as shown above.
Keep the trim so you can reverse the process if desired at a later date.
Nail to the inner frame.
Measure from the adjacent baseboard to the edge of the door.
Install the drywall onto the door.
Open the secret door and use superglue on the exposed edges of the drywall to stop any crumbling.
Cut a piece of baseboard to that length making a 45 degree miter cut along the end covering the wide gap between the door and jamb.