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Algebra Level 5

If \(f_{1}(x)=||x|-2| \) and \(f_{n}(x)=|f_{n-1}(x)-2|\) for \(n\geq2, n \in \mathbb{N}\), then find the number of solutions of the equation \(f_{2015}(x)=2\).

Notation: \( | \cdot | \) denotes the absolute value function.

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