Don't give in.
My cat did the same (but I think my cats gay...-.-) and now it doesn't even use the litter box inside. It HAS to shit OUTSIDE. So now whenever he wants out, he starts meowing like crazy for hours on end.
Its around -10F here right now, so I really dont want my cat running around outside...
The other night I stood next to the litter box and everytime he meowed, I would tap the litter box and continue staring at him.
Eventually he started doing tricks. He rolled over and everything! Then someone started walking through the house so he was all leik HOMG FRONT DOOR OPEN PL0X