Too Many Greek Letters

Algebra Level 3

The polynomial \(F(x)=x^6-2x^5+3x^{4}-4x^{3}+5x^{2}-6x+7\) has \(6\) roots, namely \(\alpha, \beta, \gamma, \theta, \sigma\) and \(\omega\). The value of \(\frac{1}{\alpha}+\frac{1}{\beta}+\frac{1}{\gamma}+\frac{1}{\theta}+\frac{1}{\sigma}+\frac{1}{\omega}\) can be expressed as \(\frac{a}{b}\), where \(a\) and \(b\) are coprime integers.

What is the value of \(a \times b\)?

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