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If you can't find a 3-inch fired shell, carry your gun into a smaller gun friendly gun store and see if they will let you try a 2 1/2 loaded shell and see if it fits.
That's not a good way to check a chamber. Shotgun chambers don't work like centerfire chambers. (It's still not the greatest idea for identifying centerfire chambers, either.)
Unfired shotgun shells are shorter than their required chamber length. As such, it is generally not just possible, but typical, for a 2.5" .410 shell to slide right into a 2" chamber; or a 12 ga 3" shell to slide into a 2-3/4" (or 2-9/16") chamber.
Using loaded ammo tells you nothing about the chamber length unless the shell refuses to fully chamber. ...And then all you know is that the chamber is substantially shorter than that shell.
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Don't even try it. It's even worse than the internet would lead you to believe.