Triangle and another triangle

Geometry Level 3

With \(a,b,c\) are the sides of a scalene triangle, and \(\mu a,\mu b,\mu c \) are the sides of a similar triangle inscribed in the former triangle.

Denote \(\theta\) as the angle between the sides \(a\) and \(\mu a\). What is the value of \(| 2 \mu \cos \theta | \)?

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