Can I connect a generic Bluetooth headphone to Xbox 360?

I have a generic Bluetooth headphone, I wonder if I can connect it to my Xbox 360 so I can play without bothering people around me with loud sounds.

I have tried to pair it with the "connect button" next to the USB ports, but nothing happens:

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Xbox 360 does not have bluetooth built in. The connect button is for controllers only and they don't use bluetooth.