#### Answer

$\theta = \frac{\pi}{3}+\pi n, \frac{2 \pi}{3}+\pi n $ are the critical numbers.

#### Work Step by Step

Find the critical numbers of $g(\theta) = 4\theta -\tan \theta$
Differentiate and set the derivative $=0$
$g'(\theta) = 4-\sec ^2 \theta$
$\sec ^2 \theta = 4$
$\sec \theta = \pm 2$
$\theta = \frac{\pi}{3}+\pi n, \frac{2 \pi}{3}+\pi n $ are the critical numbers.