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Algebra Level 4

If \({\theta}_{1},{\theta}_{2},{\theta}_{3} and {\theta}_{4}\) are four real numbers,then any root of the equation(where \(z\) is a complex number):

\(sin {\theta}_{1}{z}^{3} + sin {\theta}_{2}{z}^{2} + sin {\theta}_{3}z + sin {\theta}_{4} = 3\)

lying inside a unit circle \(\left| z \right| = 1\), always satisfies the inequality :

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