# Literally too many variables!-2

Algebra Level 4

If $$a=\dfrac{b+c}{x-2}$$, $$b=\dfrac{c+a}{y-2}$$, $$c=\dfrac{a+b}{z-2}$$, $$xy+yz+xz=67$$ and $$x+y+z=2010.$$ What is the value of $$-xyz$$?

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