Algebra vs. Trigonometry

Algebra Level 5

\[\large P=x^{2}+\sqrt{7y}-z^2-2z\]

Given that \(x,y\) and \(z\) are real numbers satisfying \[x-\sqrt{y-1}(z+1)=\sqrt{yz^2+2yz-2z^2-4z}\] and \(y\le2\), determine the maximum value of \(P\).

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