To solve for x, we first need to isolate x on one side of the equation.

We have:
ctg(x/4) = -1/√3

To isolate x, we need to take the arctangent (or inverse cotangent) on both sides of the equation:

arctan(ctg(x/4)) = arctan(-1/√3)

Since arctan(ctg(x/4)) = x/4, we get:

x/4 = arctan(-1/√3)

Now, we can multiply both sides by 4 to solve for x:

x = 4 * arctan(-1/√3)

Using a calculator, we find that:

x ≈ 5.81577 (rounded to 5 decimal places)