A rain gutter is to be constructed from a metal sheet of width 48 cm by bending up one-third of the sheet on each side through an angle θ.

Show that the cross-sectional area of the gutter is modeled by the function
A(θ) = 256 sin(θ) + 256 sin(θ) cos(θ).

For what angle θ is the largest cross-sectional area achieved?