Trig soup

Algebra Level 5

sinx+sin3x<sin5x+sin7x\sin { x} +\sin{3x}<\sin{5x}+\sin{7x}

If the ranges of solutions to this problem are in the form

αn<x<μ+βn,\alpha n<x<\mu+\beta n,

Γ+γn<x<Δ+δn,\Gamma +\gamma n<x<\Delta +\delta n,

ς+εn<x<Υ+ζn,\varsigma +\varepsilon n<x<\Upsilon +\zeta n,

χ+ηn<x<Θ+θn,\chi +\eta n<x<\Theta +\theta n,

Xi+ξn<x<Σ+σn,Xi +\xi n<x<\Sigma +\sigma n,

Ψ+ψn<x<Ω+ωn;\Psi +\psi n<x<\Omega +\omega n;

where nZ,n\in \mathbb{Z},


then

α+μ+β+Γ+γ+Δ+δ+ς+ε+Υ+ζ+χ+η+Θ+θ+Ξ+ξ+Σ+σ+Ψ+ψ+Ω+ω=\left\lfloor \alpha+\mu+\beta+\Gamma+\gamma+\Delta+\delta+\varsigma+\varepsilon+\Upsilon+\zeta+\chi+\eta+\Theta+\theta+\Xi+\xi+\Sigma+\sigma+\Psi+\psi+\Omega+\omega \right\rfloor =

...

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