Find all the solutions of the equation csc x tan x=2√3/3 on the interval [0,2π).
\(\csc x \tan x = \dfrac1{\sin x} \cdot \dfrac{\sin x}{\cos x} = \dfrac1{\cos x} \)
\(\dfrac1{\cos x} = \dfrac{2\sqrt 3}3\\ \dfrac1{\cos x} = \dfrac{2}{\sqrt 3}\\ \cos x = \dfrac{\sqrt 3}{2}\\ x = \dfrac{\pi}{6} \text{ or } x = \dfrac{11\pi}{6}\)