\(\Delta ABC\) is a triangle such that \[\sin (2A+B)=\sin (C-A)=-\sin (B+2C)=\frac{1}{2}\] If \(A\), \(B\) and \(C\) are in an arithmetic progression, then determine the values of \(A\), \(B\) and \(C\).

Enter the answer as \(A+2B+3C\) without the degree sign.

This problem is part of the set Trigonometry.

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