Answer:
Step-by-step explanation:
[tex]tan^2x+\sqrt{3} tanx=0\\tanx(tanx+\sqrt{3} )=0\\either~tan~x=0=tan~n\pi \\x=n\pi \\where~n~is~an~integer.\\if~x \in[0,2\pi )\\then~x=0,\pi \\or\\tan~x+\sqrt{3} =0\\tan~x=-\sqrt{3}=tan~(\pi-\frac{\pi }{3} ),tan~(2\pi -\frac{\pi }{3} )\\tan~x=tan(\frac{2\pi}{3} ),tan(\frac{5\pi}{3} )\\x=\frac{2\pi }{3},\frac{5\pi }{3}[/tex]
