Fantech wiring?

I have a fantech rs6 and it works but the wiring looks wrong? The fantech website shows a black and blue wire as pos/neg and a green yellow as ground. I see no green/yellow, I have 3 inlets on the fan- a black, a blue, and a brown. Currently the cord only uses the white and black wires hooked up to the fans black and blue, ive never hooked up the green wire from the cord but it always works. Should I hook the green to the brown fan terminal? It seems like I should be using that ground?
Im concerned that if I hook up the green wire from the power cord to the brown terminal it may burn the fan motor. The fan has always worked since I wired it up but the 3rd wire is extra protection so I should use it right?

Some fans don't use the earth or ground. Not sure on your location but where I am brown is a live not an earth. So don't hook up to that.
I have had a few cheap fans which had two wires you could hook the live to, the purpose is 2 speeds depending on which you want you use one of them but never both.

just put the green wire to a screw on the fan, now it's grounded. The ground on the fan is so you don't get shocked if you touch it and the power is hooked up wrong and leaking into metal of fan.

the fan is plastic, I found the manual- https://www.acwholesalers.com/hvac/pdf/fantech/fantech23-in.pdf
It looks like it only uses two of the three wires, it says since the fan motor is isolated within a plastic housing, grounding is not necessary. Now that I think of it all of my household fans only use a 2 wire cord.

Capacitor start motors have, wait for it.... capacitor. The brown wire you see is most likely just the capacitor for helping starting the motor. Leave it alone. The way it's wired up currently is correct. DO NOT PUT THE GROUND WIRE ON IT. If there's no metal housing and no ground connection, leave the ground wire disconnected/capped off.

thanks, its been running for years and when I looked at the cord it seemed odd that one wire wasnt connected.