Problem

乙、計算、證明題：共 3 題，每題 12 分，共 36 分。須詳細寫出計算及證明過程，否則不予計分。

3. A trough with a trapezoidal cross section is to be constructed with a 1-foot base and sides that are 20 feet long and 1 foot wide, as shown in the figure. Only the angle $\theta$ can be varied. What value of $\theta$ will maximize the trough’s volume?