设\(m=(2\sin {\frac {B} {2}},1),n=(\cos {B},\cos {\frac {B} {2}})\)，且\(m\)||\(n\)

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在\(\triangle ABC\)中，角\(A,B,C\)的对边分别为\(a,b,c\)，已知\(\cos {A}=\frac {3} {5}\).

设\(m=(2\sin {\frac {B} {2}},1),n=(\cos {B},\cos {\frac {B} {2}})\)，且\(m\)||\(n\)，求\(\sin \left( {B - 2C} \right)\)的值.

参考答案：\(\sin \left( {B - 2C} \right) = - \frac{{31\sqrt 2 }}{{50}}\)