Introductory Calculus Question (trig limit)

limit as x approaches zero of (1-cos^4(x ))/(sin2x)^2 = ??

I can get to

(1-cos^4(x ))/(sin2x)^2 = (1-cos^2x)(1+cos^2x) / ((2sinxcosx)(2sinxcosx))

the denominator might be wrong sin2x=2sinxcosx .

Or alternatively,

(1-cos^4(x ))/(sin2x)^2 = (1+cos^2(x ))(sin^2(x ))/sin^2 (2x)

Thanks for looking. I can't get it past there. The idea is to get to a point where things can be simplified by the following:

the lim as x approaches zero of sinx/x = 1

the lim as x approaches zero of sinx=0

the lim as x approaches zero of cosx=1