Let \(f(x)\) be a function with two properties:

(a) For any two real numbers \(x\) and \(y\), \[f(x+y) = x + f(y)\] and

(b) \(f(0)=2\)

If \(\alpha\) is a Real Number and both \(\beta\) and \(\gamma\) are positive integers

\[\arcsin (f(100)) = \alpha - i\ln(\beta+\sqrt{\gamma})\]

Evaluate \(\lfloor \alpha \beta \gamma \rfloor\).

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