For some reason, the triangle choke is my highest percentage submission.
Sometimes the pros don't SEEM to angle their triangles when they actually do it. That's because in the heat of the moment, their opponent twists around and often spins FOR them, when the bottom guy is pulling the shin down. Also, when the top guy is standing up, which often happens, it's easier for the bottom guy to spin just by a little twist of the hips, because of the lack of friction to the ground. But some guys are also just very flexible and have long legs.
Nogueira actually didn't tap Coleman with a triangle, but with a triangle armbar (i.e. he pulled on the arm after getting the triangle almost sunk). Maybe if he had spun a bit more, he could have finished the triangle, who knows?
Here's how I do my triangles:
Snake my leg past his arm on the outside or the inside, getting it on top of his neck and (usually) crossing my legs.
Grab my shin and pull it down. At the same time, I try to spin, which will help me get my shin down as far as possible. I do NOT try to get the arm across just yet.
If he tries to stand up at this point, I will spin by underhooking his leg. If he's on his knees, I will spin by posting on his hip with my foot. But sometimes I do neither of these - just pull my shin down. That's sometimes good enough when you're opponent is thrashing around because he'll spin himself into a better angle for me :) It doesn't work that well against a non-resisting opponent though.
The main thing is to keep his head down and pull my shin down.
When I feel that for the time being, I can't get my shin any lower, I go to the next step:
- Get his inside arm as far across as I can, usually using both my arms. Here's where I might very well temporarily release my grip on my shin. I raise my hips up a bit, pull the arm across and lower my hips again.
When I feel that for the time being, I can't get his arm any further across, I go to the next step:
- This step is exactly like step 2 (pulling your shin down). Only this time, since his arm is fully or partially across, you should be able to pull your shin down even further, possibly all the way down to under your knee (i.e. the optimal triangle position).
Now I pull my heels down and squeeze my knees together. If he doesn't tap, I pull his head down with both arms.
Note that this assumes that you ARE able to hold onto your shin and get his arm across. If you start to lose the hold on your shin (or didn't get it in the first place), underhook his leg and armbar him. If you're having problems getting his arm across, AFTER pulling your shin down as far as possible and spinning, you can go for an omoplata.
I've also had good success with going for the triangle armbar and going back to the triangle when my opponent clasps his hands together and drives into me.
There's lots more to it, but that's my basic idea.