Polynomial with known root sine squared

Geometry Level 5

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

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

This question is from the set polynomial with known trigo root.

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