Vieta's was fine, until this problem...

Algebra Level 4

The equation

\[x^6-7x^5+8x^4-9x^3+10x^2-11x+12=0\]

has 6 (possibly complex) roots \(a_1, a_2, ..., a_6\). Determine the value of

\[\left| \prod_{i=1}^{6} \left(a_i-1\right) \right| \]

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