To solve this equation, we will first apply the trigonometric identity:

tg(-θ) = -tg(θ)

So we have:

√3tg(3x/4 - π/6) = -1

tg(3x/4 - π/6) = -1/√3

Now we need to find the angle whose tangent is -1/√3. We know that tg(π/6) = √3, so tg(-π/6) = -√3.

Therefore, the reference angle for -1/√3 is -π/6. However, we need to find the actual angle in the interval [0, 2π] that has this tangent value.

Since the value is negative, we are looking for the angle in the third quadrant where tangent is negative.

Thus, the angle is:

3x/4 - π/6 = -π/6

3x/4 = 0

x = 0

So, the solution to the equation is x = 0.