Find real solutions of the system
sin x + 2 sin(x+y+z) = 0,
sin y + 3 sin(x+y+z) = 0,
sin z + 4 sin(x+y+z) = 0.
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We have .
Adding the first two equations and substracting the third, we have: (1)
In the same way if one of the others two factors from (1) is 0.
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