How do you install an indirect drain to the main system to prevent possible sewage back-up into a 3 compartment sink?

You must maintain a 2" air gap from indirect waste to sewer waste.

If sewage back up was the issue, I would recomend "directly" piping the 2 inch drain to the main sewage with a 2 inch normally closed backwater valve. If you piped an indirect drain you would not be protected from sewer back up. I assume this is for a sink perhaps in a basement?