сумма различных корней уравнения sin9x sin7x =sin5x sin 11x из интервала (-п;3п\4)

sinasinb=1/2(cos(a-b)-cos(a+b))1/2(cos2x-cos16x)=1/2(cos6x-cos16x)cos2x-cos16x=cos6x-cos16xcos2x-cos6x=0cosa-cosb=-2sin(a-b)/2sin(a+b)/22sin2xsin4x=0sin2x=0⇒2x=πn⇒x=πn/2sin4x=0⇒4x=πn⇒x=πn/4-общее-π<πn/4<3π/4-4<n<3n=-3⇒x=-3π/4n=-2⇒x=-2π/4n=-1⇒x=-π/4n=0⇒x=0n=1⇒x=π/4n=2⇒x=2π/4-3π/4-2π/4-π/4+0+π/4+2π/4=-3π/4