Ratio Of Different Trigonometric Functions!

Geometry Level 3

If cos3AcosA\dfrac {\cos {3A}}{\cos {A}} =12= \dfrac {1}{2}, then the value of sin3AsinA\dfrac {\sin {3A}}{\sin {A}} can be expressed as ab\dfrac {a}{b}, where aa and bb are coprime positive integers, find a+ba+b.

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