A strange equation I

Algebra Level 5

The four roots of the polynomial \(P(x)=x^{4}+8x+12\) can be expressed (with the correct choice of signs) as:

\(x=\mp\sqrt{a\cos(d°)}\pm\sqrt{\pm\sqrt{b\sec(d°)}-c\cos(d°)}\)

\(0<d<40\)

Where, \(a\), \(b\), \(c\) and \(d\) are positive integers, and \(d\) is in degrees. Find \(a+b+c+d\).

You may also try Part II.

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