Tan Roots

Algebra Level 5

Suppose the roots of the monic polynomial x892x6+134x428x2+1x^{8}-92x^{6}+134x^{4}-28x^{2}+1 are tan(miπ)\tan(m_{i}\pi) where 1i81\leq i\leq8 and 0<mi<1.0<m_{i}<1. Find the value of i=18mi.\displaystyle{\sum_{i=1}^8 m_i}.

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