Question

tan4theta = (radical 3) / 3

theta = 7pi/24, 13pi/24, 19pi/24
Let me know if im right.

Answer 1

tan4x = 1/√3
4x = π/6
x = π/24 + nπ/4
= π/24, 7π/24, 13π/24, 19π/24

Looks like you missed π/24

Answer 2

arctan(-rad3 / 3)= -pi/6 ?

Answer 3

yes, tan (-30 degrees) = -sqrt 3 / 3
but also tan (180-30) =pi-pi/6 = 5 pi/6