Let the sides opposite to angles $A , B , C$ of $\triangle A B C$ be $a , b , c$ respectively. Given $$\sin C \sin ( A - B ) = \sin B \sin ( C - A )$$ (1) If $A = 2 B$ , find $C$ ; (2) Prove: $2 a ^ { 2 } = b ^ { 2 } + c ^ { 2 }$ .
Let the sides opposite to angles $A , B , C$ of $\triangle A B C$ be $a , b , c$ respectively. Given
$$\sin C \sin ( A - B ) = \sin B \sin ( C - A )$$
(1) If $A = 2 B$ , find $C$ ;
(2) Prove: $2 a ^ { 2 } = b ^ { 2 } + c ^ { 2 }$ .