Answer
$42.5^\circ$
Work Step by Step
Step 1. Given $\alpha=59.4^\circ, k=1.33$, with $sin\alpha=k\cdot sin\beta$, we have $1.33sin\beta=sin59.4^\circ$ which gives $sin\beta=0.6472$
Step 2. Use the $sin^{-1}$ function on the above result to get $\beta=40.33$
Step 3. $\theta=4\beta-2\alpha=4\times40.33-2\times59.4\approx42.5^\circ$
