Given a \(\Delta ABC\), we define the quantities \(x, y\) & \(z\) as follows:

\(x = tan(\frac{B-C}{2}) \times tan(\frac{A}{2})\),

\(y = tan(\frac{C-A}{2}) \times tan(\frac{B}{2})\),

\(z = tan(\frac{A-B}{2}) \times tan(\frac{C}{2})\).

Find \(x + y + z + xyz\)

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