Find the value of tan√3 - cot(-√3)

Let the value of tan√3 = y
So tan(y) = √3 ⇒ y = 60° = π/3
Now, let the value of cot(-√3) = θ
If cot(θ) = √3 ⇒ θ = 30° = π/6
But, since -√3 is negative its Principal Value is (π - θ) i.e. = π - π/6 = 5π/6
Now, tan√3 - cot(-√3) = y - θ = π/3 - 5π/6 = -π/2