A Single Cell of a Bee's Honey Comb Has the Shape

Short Answer

A single cell of a bee's honey comb has the shape shown.The surface area of this cell is given by $A=6 h s+\frac{3}{2} s^{2}\left(\frac{-\cos \theta}{\sin \theta}+\frac{\sqrt{3}}{\sin \theta}\right)$ where h, s, $\theta$ are as shown in the picture.Keeping h and s fixed, for what angle, $\theta$ , is the surface area minimal? Round to the nearest one tenth of a degree.