Chapter 7 - Trigonometric Identities and Equations - 7.6 Trigonometric Equations - 7.6 Exercises - Page 720: 18

$\frac{\pi}{3}$, $\frac{5\pi}{3}$

$2\sec x+1=\sec x+3$ $\sec x+1=3$ $\sec x=2$ $\cos x=\frac{1}{2}$ Referring to the unit circle (and remembering that cosine is positive in Quadrants I and IV), we see that the only solutions in $[0, 2\pi)$ are $\frac{\pi}{3}$ and $\frac{5\pi}{3}$.