I just checked the manual for the Trio Plus and you don't need a mixer at all!
Check manual page 13, first picture. This is basically how you have to set things up:
Plug your Guitar in the Trio Plus "Guitar input"
Connect the Trio Plus "FX Send" to the Firehawk "Guitar input"
Connect the Firehawk Mono (left) jack output to the Trio Plus "FX Return"
Connect the Trio Plus "AMP output" to the Line6 Amp input OR if your Line6 Amp has an FX loop put it in the Line6 "FX Return"
Good luck!