Mathematics

Mathematics

Problem

If tan⁡θ1,tan⁡θ2,tan⁡θ3,tan⁡θ4\tan \theta_1, \tan \theta_2, \tan \theta_3, \tan \theta_4 are the roots of the equation x4−(sin⁡2β)3+(cos⁡2β)x2−(cos⁡β)x−sin⁡β=0x^4 - (\sin 2\beta)^3 + (\cos 2\beta)x^2 - (\cos \beta)x - \sin \beta = 0 Then, tan⁡(θ1+θ2+θ3+θ4)\tan(\theta_1 + \theta_2 + \theta_3 + \theta_4) , is equal to

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