Complete square biquadratic

Algebra Level 4

How many values of \(\lambda\) lie between \([-1000\pi,1000\pi]\) for which the polynomial \[x^4-2^{\tan\lambda}.x^2+(\cos\lambda+\cos2\lambda).x+2^{\tan\lambda-2}\] is the square of the quadratic trinomial with respect to \(x\) ?

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