# Trig soup

Algebra Level 5

$$\sin { x} +\sin{3x}<\sin{5x}+\sin{7x}$$

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

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

...

×