find all values in 0 is less than or equal to x is less than 2pi solve the equations: sin(2x)= -root(3)/2 and 3tan(2x)=root(3)

\(\sin 2x = -\dfrac{\sqrt3}{2}\\ \sin 2x = - \sin 60^{\circ} \\ 2x = (180+60)^{\circ}\;or\;2x=-60 ^{\circ} \\ 2x = \dfrac{4\pi}{3}rad\;or\;2x= \dfrac{5\pi}{3}rad\\ x=\dfrac{2\pi}{3}rad\;or\;x = \dfrac{5\pi}{6}rad\)

 

 

\(3\tan 2x=\sqrt3\\ \tan 2x = \dfrac{1}{\sqrt3}\\ 2x = \dfrac{\pi}{6}rad\;or\;2x=\pi + \dfrac{\pi}{6}=\dfrac{7\pi}{6}rad \\ x=\dfrac{\pi}{12}rad\; or\; x= \dfrac{7\pi}{12}rad\)

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