If you use synaptics driver you will probably have the synclient
program installed. In terminal have a look at you current touchpad settings:
$ synclient -l
You will get a list with many settings. We are interested in the "TapButtonX options". The X is for the number of fingers, so in your case "Tapbutton3". I guess it will be disabled: TapButton3 = 0
Now type in terminal
$ synclient TapButton3=2
If your touchpad supports 3-finger-tap this should work. I cannot test it because my touchpad only supports 2-finger-tap.
Possible values:
- TapbuttonX=0: X-finger-tap disabled (can be usefull, if you often touch the pad accidently while typing on keyboard)
- TapbuttonX=1: X-finger-tap = Left mouse key
- TapbuttonX=2: X-finger-tap = Middle mouse key
- TapbuttonX=3: X-finger-tap = Right mouse key