Find ALL solutions of the interval [0, 2π) tan 2x = √3/3

Question

Find ALL solutions of the interval [0, 2π)

tan 2x = √3/3

If there are some potential solutions that won't fit, please say the reason.

Thank you

Answer 1

tan2x = sqr3/3

2x = arctan(sqr3)/3) = 30 degrees

x = half 30 = 15 degrees

x= 15 ,105, 185, 285 degrees all between 0 and 360 degrees

Answer 2

tan(2x) = √3/3

Tan^-1(√3/3) = π/6

Tangent is positive in quadrants 1 and 3

So, 2x = π/6 + kπ (Tangent is periodic with period π)

x = π/12 + kπ/2

Solutions in the interval [0, 2π): π/12, 7π/12, 13π/12, 19π/12