+1504 In the diagram below, Point A is \sqrt 3 units above O. Whenever Tasha moves a point, she translates the point $\sqrt 2$ units to the right. Whenever Richard moves a point, he rotates the point clockwise about point $O$ by $60^\circ.$
In one round of transformations, Tasha moves $A$ to $A',$ and then Richard moves $A'$ to $A''.$ In another round of transformations, Richard moves $A$ to $A_1,$ and then Tasha moves $A_1$ to $A_2.$ Find $A''A_2.$
