Yup, the water ran into the crack and made a river through the untaped seam. What you'll need to do and what you should do might be a little different. Here's why. If you have disbonding showing in a 3" area, you might have disbonding starting in a 3' area. Here's what you need to do...
Get a very sharp utility knife and cut open the tape joint in the 3" area. Make sure you work hard to discover whether there is a more serious problem by cutting more than the 3" area. It won't be pretty, and this will be one deal where it'll get uglier before it gets better, always hard for anyone to appreciate or accept.
After you have a nice ugly hole in the ceiling, you'll need to patch it with new mud and tape.
You can also try to just cut the tape joint open and force mud into it, but it probably won't be an agressive enough move, and it might fail after repaint (disaster all over again). Also check to make sure your drywall didn't collapse. Usually water on 2' spans can weaken drywall and actually cause it to warp, and you might have to replace a whole section of drywall.
If you have any doubts pay someone their minimum fee (probably $150-200) and have them come out and do the repair.