Mathematics

Problem

Let

\alpha

and

\beta

be real numbers such that

-\frac{\pi}{4} < \beta < 0 < \alpha < \frac{\pi}{4}

. If

\sin(\alpha + \beta) = \frac{1}{3}

and

\cos(\alpha - \beta) = \frac{2}{3}

, then the greatest integer less than or equal to

\left( \frac{\sin \alpha}{\cos \beta} + \frac{\cos \beta}{\sin \alpha} + \frac{\cos \alpha}{\sin \beta} + \frac{\sin \beta}{\cos \alpha} \right)^2

is _____ .