Irreducible Ratio

Geometry Level pending

Let \(ABC\) be a triangle and let \(a\), \(b\) and \(c\) be the lengths of the sides opposite to the vertices \(A\), \(B\) and \(C\), respectively. If \[ a - 4b + c = 0, 2a + b - 2c = 0 ,\] then \(\sin A : \sin B : \sin C\) can be expressed as an irreducible ratio \(p:q:r\), where \(p\), \(q\) and \(r\) are positive integers. What is \(p+q+r?\)

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