How to measure Alkaline battery lifetime/capacity in practice LED circuit?
It doesn't matter what is the voltage on LEDs, 2.77 V is about right for modern LEDs. However, three alkaline batteries should be delivering at least 3.3 v to 4.5 V under this modest load, so there must be some other circuit (or just a resistor) in series with this bunch of LEDs. However, nothing of this matters, the only 76 mA is important. Your estimation is right, a battery of elements with 2200 mAh capacity (I guess these are AA-size elements) will last about 28 hours at 76 mA load rate.

EDIT: You can ESTIMATE the working time as 2200/76. It will be a good rough estimate. You can't improve it much by considering LED voltage drop over gradually depleting battery, since the exact result will depend on type of LED driver (simple resistor or DC-DC converter), actual battery capacity under specified load current (and manufacturer), and overall temperature of battery and LEDs. So any "better" estimation will be dubious at most. If you want to measure, then just measure it with a stop-watch.