Chapter 7 - Review Exercises - Page 552: 39

$x=\frac{\pi}{2}$

$3~tan^2(\frac{x}{3})-1=0$ $tan^2(\frac{x}{3})=\frac{1}{3}$ $tan(\frac{x}{3})=±\frac{1}{\sqrt 3}=±\frac{\sqrt 3}{3}$ If $0\leq x\lt2π$, then $0\leq\frac{x}{3}\lt\frac{2\pi}{3}$ $\frac{x}{3}=\frac{\pi}{6}$ $x=\frac{\pi}{2}$