cot16*cot44+cot44*cot76-cot76*cot16 = 3

or, tan46*tan74 + tan46*tan14 - tan14*tan74 = 3

or, tan46*tan74 + tan46*tan14 - tan14*tan74 + 1 = 4

or, LHS = tan74(tan46-tan14) + (1+tan46*tan14)

or, tan74(tan32)(1+tan46*tan14) + (1+tan46*tan14)

or, (1+tan46*tan14)(1 + tan32*tan74)

or, cos32*cos42/(cos46*cos14*cos32*cos74)

or, cos42/(cos46*cos14*cos74) .....(1)

now cos(x)*cos(60-x)cos(60+x) = 1/4cos(3x)

put x = 14 to get

cos46*cos14*cos74 = 1/4*cos42 putting this in (1)

we get LHS = 4 = RHS.

hence proved....

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