Given that tgx = 3, we can determine the values of sin(x) and cos(x) using the trigonometric identity:

tgx = sin(x)/cos(x) = 3

From this, we can deduce that sin(x) = 3cos(x).

Now, let's calculate sin(4x):

sin(4x) = 2 sin(2x) cos(2x)

= 2 [2sin(x)cos(x)] [2cos^2(x) - 1]

= 4sin(x)cos(x) * [2cos^2(x) - 1]

= 12cos^3(x) - 4cos(x)

Since sin(x) = 3cos(x), we substitute this value back into the equation for sin(4x):

sin(4x) = 12(3cos(x))^3 - 4(3cos(x))

= 12 * 27cos^3(x) - 12cos(x)

= 324cos^3(x) - 12cos(x)

Therefore, sin(4x) = 324cos^3(x) - 12cos(x).