Top width of gutter = `3+2*3costheta`

Perpendicular distance between to and bottom = `3sintheta`

Cross sectional area (A) of the gutter = `(3+(3+2*3costheta))/2*3sintheta`

When the area is maximum then `(dA)/(d(theta)) = 0`

`A = (3+3+2*3costheta)/2*3sintheta`

`A = 9(1+costheta)*sintheta`

`A = 9(sintheta+costheta*sintheta)`

`A = 9/2(2sintheta+2sintheta*costheta)`

(The entire section contains 162 words.)

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