Independent Variable Inequality

Geometry Level 5

\[\large (a-b)^{2}+\left(\sqrt{\theta-a^{2}} -\dfrac{16}{b}\right)^{2}\]

Given that \(a \in [0,\sqrt{\theta}]\), \(b\in \mathbb R^{+}\) and the minimum value of the expression above is 8, find the value of \(\theta\).

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