Given that \(\tan \theta \neq 1\pm\sqrt{2}\), what is the sum of all solutions (in degrees) for the following equation for \(0^\circ \le \theta \le 360^\circ\)?
\[\tan^{4} \theta+4\tan^{3} \theta-6\tan^{2} \theta-4\tan \theta+1 = 0\]

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