Let <a n> is an infinite geometric seque...

Let is an infinite geometric sequence with first term `2cotx` and common ratio `sin^2x` and `< b_n>` is an infinite geometric sequence with first term `sin2x` and common ratio `sin^2x`. If `x in (0,pi/4]` , then the minimum value of `sum_(i=1)^ooa_i-sum_(j=1)^oob_j` is

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