hey man i think its not that easy as it looks
we have apply the sereis in
1/x2-1/tan2x
now put the sereis of tan x
(1/x2 )-1/(x-x3/3)
on further solving we get lim x tends to 0 1/x2-cot 2x=9/6=2/3
further calculation is very easy i m running out of time thats y not writing it
hope u got it....