Solution:
Method 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
Method 2 -
Given - tan 6 tan 42 tan 66 tan 78
