If the angles $A,B,C$ of a $\Delta$le are in arithmetic progression and if $a,b$ and $c$ denote the lengths of the sides opposite to $A,B$ and $C$ respectively,then the value of the expression $\large\frac{a}{c}$$\sin 2C+\large\frac{c}{a}$$\sin 2A$ is

Question

$(a)\;\large\frac{1}{2}$$\qquad(b)\;\large\frac{\sqrt 3}{2}$$\qquad(c)\;1\qquad(d)\;\sqrt 3$