Problem Analysis #11

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 an isosceles triangle $ABC$ with $AB=AC=1$, let $s$ be the smallest radius such that the three disks centered at $A,B,C$ cover all three sides. For $\angle BAC=\pi/3$, $s=1/2$. For $\angle BAC=2\pi/3$, $s=\sqrt3/2$. Compute the integer

where $s_1$ is the first value and $s_2$ is the second value.