A geometry problem by Ilham Saiful Fauzi

Geometry Level 4

Let \(\tan p\) and \(\tan q\) be the roots of \(x^{2}+ax+2016=0\) for some integer \(a\). Find the value of the following. \[a\sin(2(p+q))+4030\cos^{2}(p+q)\]

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