Sin(π+4x)-sin(3π/2-4x)=0
-sin4x+cos4x=0
-2sin2xcos2x+cos²2x-sin²2x=0/cos²2x
tg²2x+2tg2x-1=0
tg2x=a
a²+2a-1=0
D=4+4=8
a1=(-2-2√2)/2=-1-√2⇒tg2x=-1-√2⇒2x=-arctg(1+√2)+πn⇒
x=-1/2arctg(1+√2)+πn/2,n∈z
a2=-1+√2⇒tg2x=√2-1⇒2x=arctg(√2-1)+πn⇒x=1/2arctg(√2-1)+πn/2,n∈z