Place the frame face down. Squeeze a drop of wood glue on each mitered surface. Spread the glue evenly with a toothpick. Clamp the frame together with the corner clamp. Wipe excess glue from the corner.
Drill three pilot holes, two into one side of the frame and one in the other, spaced so they don’t collide with each other. Make the holes with a bit sized to the diameter of the brads you are using.
Coat each brad lightly in glue, insert it in the pilot hole and hammer it until the nail only protrudes slighty. Set the nail below the surface with a nail set and cover the hole with putty to match the frame.