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Without expanding at any stage, evaluate...

Without expanding at any stage, evaluate the value of the determinant
`|{:(2,tanAcot B+cotAtanB,tanAcotC+cotAtanC),(tanBcotA+cotBtanA,2,tanBcotC+cotBtanC),(tanCcotA+cotCtanA,tanBcotC+cotBtanC,2):}|.`

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