cot(x) = 1/tan(x) = -1/√3
so
tan(x) = -√3
Recall the range of the inverse tangent: for all real x,
-π/2 ≤ arctan(x) ≤ π/2
This means we cannot just take the inverse tangent of both sides, because that would give us an angle that's not in the interval π/2 ≤ x ≤ π.
To work around this, add π to each side of the inequality:
π/2 ≤ π + arctan(x) ≤ 3π/2
So to solve our equation, we can take the inverse tangent of both sides, but we need to add π to the right side to make sure we get the angle in the right interval:
tan(x) = -√3
becomes
x = π + arctan(-√3)
Now, arctan(-√3) = -π/3, so the solution to our equation is
x = π + (-π/3) = 2π/3
