Painting inside the closet – what a pain! There’s just not enough room to paint. Removing the sliding doors would really help. How do you do this?
Sliding closet doors are held in place by a roller / track assembly at the top and a simple retainer / glide at the bottom. Start by removing the plastic or metal retainer / guide at the base of the outer door. This small bracket is screwed into the floor, and you can remove it by loosening a few screws. Once you’ve removed the bracket, you can swing the bottom of the door in or out.

Now, from the outside, lift the door and roller off the track and move it inside the closet by perhaps a half-inch. At the same time, swing the bottom of the door out and lower the top of the door away from the track. Now you are holding the door in your hand and you can place it aside. Repeat the operation for the inner door.
After completing your paint job, reinstall the door in reverse order: tip inward at the top and hang the rollers, then tip the door into place. Re-install the lower bracket when both doors are in place.