$\large \begin{cases} x = a \sec^3 \beta \ \tan \beta \\ y = b \tan^3 \beta \ \sec \beta \end{cases}$

Given the above, find $\sin^2 \beta$.

**Details and assumptions:**

- $a$, $b$, $x$, $y$, $\sin\beta$, $\cos\beta ≠ 0$.

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