# 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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