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sin^2x+sin^2y=1/4; x-y=5pi/6

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The solution

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   2         2         
sin (x) + sin (y) = 1/4
$$\sin^{2}{\left(x \right)} + \sin^{2}{\left(y \right)} = \frac{1}{4}$$
        5*pi
x - y = ----
         6  
$$x - y = \frac{5 \pi}{6}$$
x - y = (5*pi)/6
Numerical answer [src]
x1 = -1.695261211857583e-23
y1 = -2.617993877991494
x2 = 6.283185307179586
y2 = 3.665191429188092
x3 = 12.04277183876087
y3 = 9.42477796076938
x4 = -31.41592653589793
y4 = -34.03392041388943
x5 = -3.141592653589793
y5 = -5.759586531581288
x6 = 5.759586531581288
y6 = 3.141592653589793
x7 = 2.617993877991494
y7 = 1.695261527247871e-23
x8 = 59.16666164260777
y8 = 56.54866776461628
x9 = 34.03392041388943
y9 = 31.41592653589793
x10 = -56.54866776461628
y10 = -59.16666164260777
x11 = -3.665191429188092
y11 = -6.283185307179586
x12 = -9.42477796076938
y12 = -12.04277183876087
x13 = 18.84955592153876
y13 = 16.23156204354727
x14 = -16.23156204354727
y14 = -18.84955592153876
x14 = -16.23156204354727
y14 = -18.84955592153876