What angle do I insert iPad SIM eject tool into new iPad to get the tray out?

PUSH!

The old way was to insert the tool at an angle and kind of push sideways and pull out at the same time, using leverage, and the tray would hang onto and come out with the tool, but with the new iPad (2012), simply insert the SIM eject tool straight into the tiny hole (straight being the way it enters with the least resistance, i.e. perpendicular to the case where the hole is), and then push. The tray will eject.

I'd have posted a link to authoritative information, but I just had this exact problem myself (UPS guy arrived an hour ago!) and so I'm speaking from first-hand experience :-)

I tried what I thought was obvious once I realized the hole was no longer part of the SIM card tray assembly (see photos below), so angling and pulling would do nothing like it did on the 2010 model's tray (i.e. when the hole was part of the tray).

• SIM card tray outer view from my original iPad (2010):
  
  
  Notice the hole was part of the tray.

• SIM card tray outer view from my new iPad (2012):
  
  
  Notice the hole is separate from the tray.  Insert SIM tool, and push.

I'm adding a comment. Once you notice the Sim Tray lifting just a fraction you are half way there - now push harder and it pops right out. Good luck.

The eject tool must be at an angle (slihgtly larger than 45 degrees). I just did it on my "new" iPad bought at Apple store in April 2012.

Apple support pages have instructions for the iPad 2. I could not find instructions specific for the new iPad, but the information in the previous link seems (to me) to be applicable.