Answer
$\sqrt 3$
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 $\dfrac{ 7 \pi}{3}-\dfrac{6\pi}{3}=\dfrac{\pi}{3}$
So, $ \tan \dfrac{ \pi}{3}=\sqrt 3$
Adding $n\pi$ to the angle will not change the value of the tangent function, since it repeats every $\pi$ or $180^{\circ}$.
