Big toothy grins shouldn't be forced, it should be natural, and if it doesn't come naturally then you probably haven't been happy enough. I'm fairly morose, I smile at people in that no-teeth, polite smile when I say 'good morning', but the only time I toothy-grin is when someone makes me laugh.
Maybe you should work on your smiling muscles, like just try a no-tooth smile at people, like when you buy something at a store, give the cashier a friendly little smile... like be prepared to smile at people. A smile is reasuring, it tells people that your not intending to skin them and wear them as a scarf, it gives a better impression and makes people more relaxed when your around. Tooth-grinning is not a vital skill, appearing pleasant and approachable IS!
Just try it, the next person you interact with, when you would usually say 'thank you', give them a little smile. Also try smiling when talking on the telephone, it makes your voice sound positive and friendly. At the end of the day, it's just your face - you can be as pee'd off as you like under the surface.