Find the general solution to squareroot3tan(pi/6 - 3x)-1=0

please show step by step :3

sqrt(3) tan (pi/6 - 3x) - 1 = 0
sqrt(3) tan (pi/6 - 3x) = 1
tan (pi/6 - 3x) = 1 / sqrt(3)

tan u = 1 / sqrt(3) at pi/6 and 7pi/6 = pi/6 + n * pi, where pi is an integer
let u = pi/6 - 3x

so pi/6 - 3x = pi/6 + n * pi
-3x = n * pi (subtracting pi/6 from each side)
x = -n / 3 * pi

since n is an integer, then we can drop the negative

x = n * pi/3 <=== general solution (integral multiples of pi/3)

sqrt(3) * tan(pi/6 - 3x) - 1 = 0
sqrt(3) * tan(pi/6 - 3x) = 1
tan(pi/6 - 3x) = 1 / sqrt(3)
tan(pi/6 - 3x) = tan(pi/6 + pi * k)
pi/6 - 3x = pi/6 + pi * k
-3x = pi * k
x = (-k/3) * pi

k is some integer