lim(x->0)(1/(sinx)^2-1/x^2)
=lim(x->0)[x^2-(sinx)^2]/x^4
=lim(x->0)(x+sinx)/x*lim(x->0)(x-sinx)/x^3
=2lim(x->0)(1-cosx)/(3x^2)
=2/3*lim(x->0)1/2x^2/x^2
=1/3