Definite integral Problem 2

Calculus Level 4

\[\large \int_{1}^{16} \tan^{-1} \sqrt{\sqrt x - 1} \, dx \]

Given that the integral above is equal to \( a \pi - 2\sqrt b\), where \(a\) and \(b\) are rational numbers, find the value of \(a\times b\).

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