Sin3x/sinx-sinx/sin3x=2cos2x

$\frac{sin3x}{sinx} - \frac{sinx}{sin3x}=2cos2x \\ \\ \frac{sin^23x-sin^2x}{sinx*sin3x}=2cos2x \\ \\ \frac{(sin3x-sinx)(sin3x+sinx)}{sinx*sin3x}=2cos2x\\ \\ \frac{2sinx*cos2x*2sin2x*cosx}{sinx*sin3x}=2cos2x\\ \\ \left \{ {{\frac{2cos2x*sin2x*cosx}{sin3x}=cos2x} \atop {sinx \neq 0}} \right. \\ \\ \left \{ {{\frac{cos2x*(2sin2x*cosx-sin3x)}{sin3x}=0} \atop {sinx \neq 0}} \right. \\ \\ \left \{ {{\frac{cos2x*(2sin2x*cosx-sin(2x+x))}{sin3x}=0} \atop {sinx \neq 0}} \right.$
$\left \{ {{\frac{cos2x*(2sin2x*cosx-(sin2x*cosx+cos2x*sinx))}{sin3x}=0} \atop {sinx \neq 0}} \right. \\ \\ \left \{ {{\frac{cos2x*(sin2x*cosx-cos2x*sinx)}{sin3x}=0} \atop {sinx \neq 0}} \right. \\ \\ \left \{ {\frac{cos2x*sin(2x-x)}{sin3x}=0} }\atop {sinx \neq 0}} \right. \\ \\ \left \{ {{\frac{cos2x*sinx}{sin3x}=0} \atop {sinx \neq 0}} \right. \\ \\ \{ {{\frac{(1-2sin^2x)*sinx}{sin3x}=0} \atop {sinx \neq 0}} \right.$
$\{ {{sin^2x= \frac{1}{2}} \atop {sinx \neq 0,sin3x \neq 0}} \right. \\ \\ \{ {{sinx= (+/-)\frac{ \sqrt{2} }{2}} \atop {sinx \neq 0,sin3x \neq 0}} \right. \\ \\ \{ {{x= \frac{ \pi }{4}+ \frac{ \pi n}{2} ,nEZ} \atop {x \neq \frac{ \pi k}{3},kEZ }} \right.$
x = π/4 + πn/2, n ∈ Z