When it's trained in Speed in Special Attack
Tangrowth can't learn Tri Attack, but can use it by Nature Power.
I'd have to say no to Nature Power. Tri-Attack doesn't really add anything to Tangrowth, since it gets no super-effective hit. You'd be better off using a Stat move like Sleep Powder.
The choices depend on whether you have Sun support from your team or not.
Its Ok. Tangrowth Special Moveset:
Focus Blast: Coverage.
Energy Ball: STAB
Hidden Power Rock: Coverage.
Wait, tangrowth Cant Even Learn Tri Attack!