Complete square biquadratic

Algebra Level 4

How many values of λ\lambda lie between [1000π,1000π][-1000\pi,1000\pi] for which the polynomial x42tanλ.x2+(cosλ+cos2λ).x+2tanλ2x^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 xx ?

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