(a) Differentiate the result of Problem 55 to show that the maximum value of occurs when...

(a) Differentiate the result of Problem 55 to show that the maximum value of ϕ occurs when the incidence angle θ is given by cos²θ = 1/3 (n² – 1).
(b) Use this result and that of Problem 55 to find the maximum ϕ in a raindrop with n = 1.333. This is the angle at which the rainbow appears, as shown in the Application on pages 573–574.