Prove that

Tan6 Tan42 Tan66 Tan78 =1

 Use Trigonometric Identity

tanx * tan(60 - x) * tan(60 + x) = tan(3x)

set x = 6

tan6 * tan54 * tan66 = tan18 .................... ((1))

Similarly, set x = 18

tan18 * tan42 * tan78 = tan54 ...................... ((2))

((1)) * ((2)):

tan6 * tan54 * tan66 * tan18 * tan42 * tan78 = tan18 * tan54

tan6 * tan66 * tan42 * tan78 = 1

PROVEN