Answer:Final answer is [tex]x=0[/tex] and [tex]x=2\pi[/tex].Step-by-step explanation:Given equation is [tex]3\cdot\sec\left(x\right)-2=1[/tex]Now we need to find the solution of [tex]3\cdot\sec\left(x\right)-2=1[/tex] in given interval [tex][0, 2\pi ][/tex].[tex]3\cdot\sec\left(x\right)-2=1[/tex][tex]3\cdot\sec\left(x\right)=1+2[/tex][tex]3\cdot\sec\left(x\right)=3[/tex][tex]\frac{3\cdot\sec\left(x\right)}{3}=\frac{3}{3}[/tex][tex]\sec\left(x\right)=1[/tex]which gives [tex]x=0[/tex] and [tex]x=2\pi[/tex] in the given interval.Hence final answer is [tex]x=0[/tex] and [tex]x=2\pi[/tex].