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Algebra Level 5

\[{\left| \begin{matrix} { \left( a-x \right) }^{ 2 } & { \left( a-y \right) }^{ 2 } & { \left( a-z \right) }^{ 2 } \\ { \left( b-x \right) }^{ 2 } & { \left( b-y \right) }^{ 2 } & { \left( b-z \right) }^{ 2 } \\ { \left( c-x \right) }^{ 2 } & { \left( c-y \right) }^{ 2 } & { \left( c-z \right) }^{ 2 } \end{matrix} \right| =-\frac { 351 }{ 8 } }\]

If \(x,y,z\) are roots of the equation \( {8X^3-62X^2+43X-7=0} \), and they satisfy the determinant above, where \(a,b\) and \(c\) are distinct numbers, find the value of \(|(a-b)(b-c)(c-a)|\).

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