Answer
The possibles directions are: $\theta=45^{\circ}~or~135^{\circ}~or~225^{\circ}~or~315^{\circ}$
Work Step by Step
$|A_x|=|A_y|$, so:
. $A_x=A_y$,
$\theta=tan^{-1}(\frac{A_y}{A_x})=tan^{-1}1= 45^{\circ}~or~45^{\circ}+180^{\circ}=225^{\circ}$
or
$A_x=-A_y$,
$\theta=tan^{-1}(\frac{A_y}{A_x})=tan^{-1}(-1)= 135^{\circ}~or~135^{\circ}+180^{\circ}=315^{\circ}$
