my attempt
sin 3x = cos(x+pi/4)
sin 3x= sin{ pi/2- (x+pi/2)}
sin 3x= sin( pi/4 - x )
gives
3x=pi/4 - x
x=pi/16
i have plotted this function, sin(3x) - cos(x + pi/4) = 0, for x = 0 to 2pi
it does have 6 roots for x = 0 to 2 pi
using the sum to product formula, we have this
-2 sin (pi/8 -2x) cos (x + pi/8) = 0
this one form does not generate the 6 roots as shown in the plot, i wonder