Trig[o]nometry!

Geometry Level 4

\[\displaystyle 4\cos(36^\circ) + \cot(7.5^\circ) = \sqrt a + \sqrt b + \sqrt c + \sqrt d + \sqrt e + \sqrt f\]

If the equation above is true for positive integers \(a,b,c,d,e\) and \(f\), find the value of \(a^2+b^2+c^2+d^2+e^2+f^2\).

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