Trigonometry! #132

Geometry Level 3

$$\Delta ABC$$ 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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