Problem Analysis #24

Return a single integer only. The problem has been revised so that no final answer is an irrational number, a parameterized expression, a range, a proof, a drawing, a graph, a locus equation, or a region description.

In the complex cubic problem, one endpoint of the possible range of $\sin\theta$ is $23/27$, and the relevant area is $4\sqrt3$. Encode the endpoint $23/27$ by $23+27$, and encode the area by squaring it. Find the sum of the two encoded integers.