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Find the minimum value of the function `f(x)=(pi^2)/(16cot^(-1)(-x))-cot^(-1)x`

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`f(x) = (pi^(2))/(16 cot^(-1) (-x)) - (pi - cot^(-1) (-x))`
`= cot^(-1) (-x) + (pi^(2))/(16 cot^(-1) (-x)) - pi`
`= (sqrt(cot^(-1) (-x)) - (pi)/(4sqrt(cot^(-1) (-x))))^(2) + (pi)/(2) - pi ge - (pi)/(2)`
`f_("min") = -(pi)/(2)`
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