Math Help - Minimum Surface Area of a Honeycomb

1. Minimum Surface Area of a Honeycomb

2. $S'(\theta) = \frac{3s^2}{2}\left[\frac{\sin^2{\theta} - (\sqrt{3}-\cos{\theta})\cos{\theta}}{\sin^2{\theta}}\right]$

$S'(\theta) = 0$ if

$\sin^2{\theta} - (\sqrt{3}-\cos{\theta})\cos{\theta} = 0$

$\sin^2{\theta} - \sqrt{3}\cos{\theta} + \cos^2{\theta} = 0$

$1 - \sqrt{3}\cos{\theta} = 0$

$\theta = \arccos\left(\frac{1}{\sqrt{3}}\right)$