You can beat Protoss #10 one of three ways. Please note that the following is the way I do it, and I've been playing RTS games for a very long time, and are not the right or wrong way of doing it, just ways I've found easiest.
#1 - Terran with Protoss support
For this one start by building a medium to heavy defense at your Protoss base. This would consist of 12 Pylons, 24-36 Cannons, and your DTs to help defend the area, move Tassadar and Zeratul to the back of your base for safty. Start massing Probes and mine your ass off. DONT forget about your Terran base! They will direct 85-90% of their heavy attacks on your Terran base. For your Terran defense you will need 12 bunkers, 6-12 Tanks, 12 SCVs(to keep things healthy), 6 Observers(move them around the Zerg base, duh), 48 Ghosts (or Marines, I go Ghosts because with upgrades they have the same range as Guardians), and throw in some Turrets for added defense. NEVER leave an area open, they will try every way into your base, defense is the key.
Now that you have a solid defense, you must work on your army. This should be made up of 24 Tanks, 12 SCVs, 6-12 Wraiths, Raynor, and 6 Observers. Depending on how well you protected your Terran base will depend on the supply you have, but you should have enough. Now slowly advance your tanks with the air support for Guardians. Make a DIRECT path to the Overmind! You do not need to kill everything, just the overmind. If you do it right, you should beat it no worries.
#2 - Protoss with Terran support
Defend your bases as in #1. This time mass SCVs to mine.
For this one, mass Reavers with Scout (or Wraith) support. Attack the same way you did with the tanks. Easy huh?
#3 - When in need...
Forget #1 and #2 and use the blasted CHEATS! That's why the have them, duh man.
power overwhelming
Nuff said!