The minimum value of \( (\tan A-\cos \mathrm{B})^{2}+(\cot A-\sin B)^{2} \), where \( A \) and \...

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The minimum value of \( (\tan A-\cos \mathrm{B})^{2}+(\cot A-\sin B)^{2} \), where \( A \) and \( B \) are independent variables, is of the form \( a-b \sqrt{c} \), where \( a, b, c \) are natural numbers. The value of \( a+b+c \) is equal to
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