How do I detach the antenna box in order to disassemble it?

It should be held inside the car by a bracket with a screw. Remove that first. To find this bracket/screw you'll need to pull out the plastic panel that covers the antenna motor inside the trunk, in the driver's side wheel well.

Then, you need to loosen the nut that holds the antenna in place on the outside of the car. It is sort of hidden, as it looks like it's not really a nut. Shown here is an example below:

See that part with a flat side just below the tip of the recessed antenna? That should unscrew, using the an open end wrench of the correct size.

Now, it's good to know there is another style of nut that you may run in to depending on your car. Instead of a flat portion to get an open end wrench around, you may instead find two "slots" in the nut. This kind needs a special spanner wrench that fits over the tip of the antenna. Or, alternatively, you can carefully and slowly "tap" the nut off with a punch and hammer. Just use the punch to tap the nut in the direction it would turn to loosen. Lefty loosey!