Fraction of Fraction

\[ \large a + \frac{1}{b + \frac{1}{c + \frac{1}{d}}} = \dfrac{229}{99} \]

If \(a, b, c\) and \(d\) are positive integers satisfying the equation above, find the value of \(a^{2} + b^{2} + c^{2} + d^{2}\).

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