Hi, I need to find the limit as x->0 of 1/(1-Cosx)-2/x^{2}(I know it's 1/6, but I need to figure out how to get there).

I think I need to make use of the limits (all as x->0) sinx/x=1, tanx/x=1, and (1-cosx)/x=0.

So far, I've tried multiplying the 1/((1-cosx) term by it's conjugate (1+cosx)/(1+cosx) and combined the fractions, but this hasn't really gotten me anywhere useful yet. I've also tried using l'hopitals, but the limit just gets uglier and uglier with each application. Any ideas?