# INMO - 1991; Part - 1

Geometry Level pending

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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