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1. Area of polygon from cyclotomic roots ●●●○○ 50 ptsLet $P$ be the convex polygon in the complex plane whose vertices are the roots of $z^7 + z^6 + z^5 + z^4 + z^3 + z^2 + z + 1 = 0$. The area of $P$ can be expressed in the form $\frac{a + b \sqrt{c}}{d}$, where $a$, $b$, $c$, $d$ are positive integers, in simplest form. Find $a + b + c + d$.