That's a Challenge!

Geometry Level 4

\[\large Q = \dfrac { a }{ c } \sin { 2C }+ \dfrac { c }{ a } \sin { 2A } \]

If the angles \(A\),\(B\) and \(C\) of a triangle are in an arithmetic progression and let \(a\), \(b\) and \(c\) denote the lengths of the sides opposite to \(A\), \(B\) and \(C\) respectively, then find the value of \(Q\).

Give your answer to 3 decimal places.

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