## Essential University Physics: Volume 1 (4th Edition)

$\theta = 54.74^{\circ}$
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: $$0=\frac{(2+tan^2\theta)(sec(2\theta))-tan\theta(2tan\theta sec2\theta)}{(2+tan^2\theta)^2}$$ $$0=\frac{(2sec(2\theta))-tan^2\theta sec2\theta)}{(2+tan^2\theta)^2}$$ $$\theta = 54.74^{\circ}$$