Answer
$\dfrac{\sqrt 3}{3}$
Work Step by Step
The reference angle of an angle $0 \leq \theta \lt 2\pi $ based on its position can be computed by using the following steps:
a) Quadrant- I: $\theta $
b) Quadrant -II: $(\pi-\theta)$
c) Quadrant- III: $(\theta - \pi)$
d) Quadrant - IV: $(2\pi - \theta)$
Thus, the reference angle of $\dfrac{ 6 \pi}{3}+\dfrac{3\pi}{3}-\dfrac{ 8\pi}{3}=\dfrac{\pi}{3}$
So, $ \cot \dfrac{ \pi}{3}=\dfrac{1}{\tan \dfrac{ \pi}{3}}=\dfrac{\sqrt 3}{3}$
Thus, we have $ \cot \dfrac{\pi}{3}=\dfrac{\sqrt 3}{3}$ because $\theta$ lies in Quadrant-III.
