8sinx*cosx+sin2x*cos4x=0
4*(2sinx*cosx)+sin2x*cos4x=0
4*sin2x+sin2x*cos4x=0
sin2x*(4+cos4x)=0
sin2x=0 или 4+cos4x=0
1. sin2x=0, 2x=πn, n∈Z.|:2 x=πn/2, n∈Z
2. 4+cos4x=0, cos4x=-4 решений нет -4∉[-1;1]
по условию x∈[80°;270°]
80°≤180° *n/2≤270°
80°≤90° n≤270° |:90°
8/9≤n≤3.
n=1, x₁=π/2
n=2, x₂=2π/2=π
n=3, x₃=3π/2
x₁+x₂+x₃=π/2+π+3π/2=6π/2=3π
3π=3*180°=540°