There's an episode where Tori and Robbie got stuck in Nozu because Robbie couldn't pay for their meal where the cast discussed how Trina got in. Sikowitz apparently was hallucinating from drinking coconut milk during Trina's audition that he believed that she was incredibly talented when she wasn't.
And though in many episodes where it shows that Trina can't sing, apparently she can sing the song "Five Fingers to the Face" in the show at least twice (once with Cat when they were picking up the solvent for Tori because her makeup had industrial glue on it and another in a party bus with the rest of the cast when Tori had to find a ride to school) without her sounding like she's choking a cat. I guess that's the only song she can sing.
Hmmmm i guess she........... she............ she........................ maybe she was talented back when she got in Hollywood Arts but then she lost her talent? i mean like its not the ACTUAL ANSWER but its my opinion
You gotta remember if it wasnt for Trina being in HA Tori woulda never been in there. So maybe the principal saw in a dream that Tori would go to HA if he let in Trina...
Or maybe the HA students were bad so he let Trina in to get back at them. Idk this is a good question I've been wondering the answer myself.