Question 1155360
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The key to the solution is this identity  tan(x) = {{{1/tan(pi/2-x)}}}.


It gives


    tan(6°)*tan(84°) = 1

    tan(12°)*tan(78°) = 1

    tan(18)*tan(72°) = 1

    . . . and so on . . . 

    tan(42°)*tan(48°) = 1.



By multiplying all these identities, you will get finally


    tan(6°)*(tan(12°)*tan(18°)* . . . *tan(84°) = 1.


<U>ANSWER</U>.  This product is equal to 1.
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Solved.