Помогите решить систему sinx/siny=1 x-y=pi/3

[latex] \left \{ {{sinx=siny} \atop {x-y= \frac{ \pi }{3}}} \right. [/latex] [latex] \left \{ {{sinx-siny=0} \atop {x-y= \frac{ \pi }{3}}} \right. [/latex] [latex] \left \{ {{2cos(\frac{x+y}{2})*sin(\frac{x-y}{2})=0} \atop {x-y= \frac{ \pi }{3}}} \right. [/latex] [latex] \left \{ {{2cos(\frac{x+y}{2})*sin(\frac{ \pi }{6})=0} \atop {x-y= \frac{ \pi }{3}}} \right. [/latex] [latex]cos(\frac{x+y}{2})=0[/latex] [latex]\frac{x+y}{2}=\frac{ \pi }{2}+ \pi k[/latex] [latex]x+y=\pi+2 \pi k[/latex] [latex]x-y= \frac{ \pi }{3}[/latex] Сложим два последних уравнения: [latex]2x=\pi+2 \pi k+\frac{ \pi }{3}[/latex] [latex]2x=\frac{4 \pi }{3}+2 \pi k[/latex] [latex]x=\frac{2 \pi }{3}+ \pi k[/latex] [latex]y=x-\frac{\pi }{3}=\frac{2 \pi }{3}+ \pi k-\frac{\pi }{3}=\frac{\pi }{3}+\pi k[/latex] k∈Z