To solve this trigonometric equation, we can first isolate the trigonometric function by dividing both sides by sqrt(3):

Tg(pi/4 + 4x) = sqrt(3) / sqrt(3)
Tg(pi/4 + 4x) = 1

Next, we know that tan(pi/4) = 1, so we can rewrite the equation as:

Tg(pi/4 + 4x) = tg(pi/4)

Since the period of the tangent function is pi, we can set pi/4 + 4x = pi/4 + n*pi for any integer n.

By solving for x, we get:

pi/4 + 4x = pi/4 + npi
4x = npi
x = n*pi / 4

Therefore, the solution to the equation is x = n*pi / 4 for any integer n.