Trig soup

Algebra Level 4

\(\sin { x} +\sin{3x}<\sin{5x}+\sin{7x}\)

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

\(\alpha n<x<\mu+\beta n,\)

\(\Gamma +\gamma n<x<\Delta +\delta n,\)

\(\varsigma +\varepsilon n<x<\Upsilon +\zeta n,\)

\(\chi +\eta n<x<\Theta +\theta n,\)

\(Xi +\xi n<x<\Sigma +\sigma n,\)

\(\Psi +\psi n<x<\Omega +\omega n;\)

where \(n\in \mathbb{Z},\)


then

\(\left\lfloor \alpha+\mu+\beta+\Gamma+\gamma+\Delta+\delta+\varsigma+\varepsilon+\Upsilon+\zeta+\chi+\eta+\Theta+\theta+\Xi+\xi+\Sigma+\sigma+\Psi+\psi+\Omega+\omega \right\rfloor =\)

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