Play video content EXCLUSIVE TMZ.com

Jax Taylor is a cooked goose in his felony theft case ... at least that's the way it appears from surveillance video in the store.

TMZ obtained the video, which precisely shows Jax doing his handiwork at Freaky Tiki Tropical Optical in Honolulu. It's clear as can be ... he grabs a pair of Polaris shades, meanders a bit ... then books it out of the store.