applecare

AppleCare+ can be purchased with or without Loss and Theft protection. If you purchased it with you don’t need insurance through your provider, as the it is the same insurance your network provider offers.

Here are more details:AppleCare Products - iPhone - Apple

So, almost certainly, the answer is no, you do not need both. But you need to make that final assessment, based on the terms and conditions of AppleCare+, and those offered by your carrier's insurance plan. You have got to assess whether the carrier's coverage is coextensive with AppleCare+, and, if so (or even if not), which one offers better terms (not just about repairs generally, but accidental damage, other kinds of loss, or theft, if applicable and replacement policies. It's kind of like trying to determine whether your home owner's policy covers you in a rental car, and whether any supplemental insurance from the car company is needed.

JDee

The decision is up to you, but I wouldn't reccomend it. Your just paying for something you would get through Apple. Unless its a better deal (cheaper, covers more than 2 accidents a year), AppleCare works fine.

Most likely not but you should compare the coverage of both plans and decide for yourself. For example, your AppleCare plan may or may not include theft and loss coverage and I have no idea what coverage the plan offered by your cell provider includes.

You would have to call and ask. The number is in that link.