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.