Quadratic and Trigonometry for JEE #2

Algebra Level 4

Let \(x\) and \(y\) be the roots of the equation \[ a \sin^{2}\theta + b \sin\theta +c =0\] such that \[\sin x + 2 \sin y = 1\] then find the value of \[(2015)*( a^{2}+2b^{2}+3ab+ac)\]

Given that a,b,c are real numbers such that \(a\neq 0\).

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