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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