sin²x+sin²(2П+П/3-x)=3/2

x+y=7П/3

sin²x+sin²(П/3-x)=3/2

y=7П/3-x

sin²x+(sinП/3cosx-sinxcosП/3)²=3/2

sin²x+(3/4)cos²x+(1/4)sin²x-(√3/2)sinxcosx=6/4

sin²x-(3/4)sin²x+(1/4)sin²x-(√3/2)sinxcosx=3/4

(1/2)sin²x-(√3/2)sinxcosx=3/4sin^2x+3/4cos²x

(1/4)sin²x+(3/4)cos²x+(√3/2)sinxcosx=0

cos^2x((1/4)tg²x+3/4+(√3/2)tgx)=0

(1/4)tg²x+3/4+(√3/2)tgx=0

tgx=t

t²/4+(√3/2)t+3/4=0

t²+2√3t+3=0

(t+√3)²=0

tgx=-√3

x=-П/3

y=7П/3-x=7П/3+П/3=8П/3

(-П/3; 8П/3)