Given:
[tex]\tan 3x=1,\lbrack0,2\pi)[/tex]
To find the value of x:
Solving we get,
[tex]\begin{gathered} \tan (3x)=1 \\ 3x=\frac{\pi}{4},\frac{5\pi}{4},\frac{9\pi}{4},\frac{13\pi}{4},\frac{17\pi}{4},\frac{21\pi}{4} \\ x=\frac{\pi}{12},\frac{5\pi}{12},\frac{3\pi}{4},\frac{13\pi}{12},\frac{17\pi}{12},\frac{7\pi}{4} \end{gathered}[/tex]
Hence, the answers are,
[tex]x=\frac{\pi}{12},\frac{5\pi}{12},\frac{3\pi}{4},\frac{13\pi}{12},\frac{17\pi}{12},\frac{7\pi}{4}[/tex]
