# Polynomial with known root cosine

Geometry Level 5

$ax^4 - bx^3 - cx^2 + dx + 1$

You are given that the polynomial above has a root of $$\cos\left(\frac{2\pi}{15}\right)$$ for positive integers $$a,b,c$$ and $$d$$. Find the value of $$a+b+c+d$$.

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