Answer
$\theta = 54.74^{\circ}$
Work Step by Step
In problem 53, we found the following expression:
$$\mu = \frac{tan\theta}{2+tan^2\theta}$$
Thus, we take the derivative and set it equal to zero to find:
$$0=\frac{(2+tan^2\theta)(sec(2\theta))-tan\theta(2tan\theta sec2\theta)}{(2+tan^2\theta)^2}$$
$$0=\frac{(2sec(2\theta))-tan^2\theta sec2\theta)}{(2+tan^2\theta)^2}$$
$$\theta = 54.74^{\circ}$$
