A strange equation II

Algebra Level 5

The three real roots of the polynomial P(x)=x33x2+1P(x)=x^{3}-3x^{2}+1 can be expressed as:

x1=bcos(e°)+a,x2=ccos(f°)+a,x3=dcos(g°)+a, x_{1}=-b\cos(e°)+a , x_{2}=-c\cos(f°)+a, x_{3}=d\cos(g°)+a,

where x1<x2<x3x_{1}<x_{2}<x_{3}, 0°<e<90°0°<e<90°, 0°<f<90°0°<f<90°, 0°<g<90°0°<g<90°, such that aa, bb, cc, dd, ee, ff and gg are positive integers; and ee, ff and gg are integer degrees. Find a+b+c+d+e+f+ga+b+c+d+e+f+g.

You may also try Part III.

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