$$ABC$$ is a triangle such that
$$$\sin \left( {2A + B} \right) = \sin \left( {C - A} \right) = \, - \sin \left( {B + 2C} \right) = {1 \over 2}.$$$
If $$A,\,B$$ and $$C$$ are in arithmetic progression, determine the values of $$A,\,B$$ and $$C$$.
Answer
$${45^ \circ },\,\,\,{60^ \circ },\,\,\,{75^ \circ }$$