Tan Roots

Algebra Level 5

Suppose the roots of the monic polynomial \(x^{8}-92x^{6}+134x^{4}-28x^{2}+1\) are \(\tan(m_{i}\pi)\) where \(1\leq i\leq8\) and \(0<m_{i}<1.\) Find the value of \(\displaystyle{\sum_{i=1}^8 m_i}.\)

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