A corner reflector is to be made from a triangular prism with index of refraction $\backslash ($ n$=2\mathrm{.}26\backslash ),$ as shown in the diagram below, where the path of a laser beam reflecting off the corner cube is shown. Corner cubes are highly useful in optics because the outgoing angle $\backslash (\backslash$phi $\backslash )$ is always equal to the incoming angle $\backslash (\backslash$theta $\backslash )($you should be able to show this!$).$ However, to get a lot of reflected power, the incoming angle can't be too large.

$9$ What is the maximum angle $\backslash (\backslash$theta $\backslash )$ with respect to the normal to the front surface of the prism such that total internal reflection occurs off the back surfaces of the corner reflector? Give your answer in degrees.