Trigonometric sum with cubic equation.

[man111]

Let [tex]-\frac{\pi}{4}\leq x,y\leq\frac{\pi}{4}[/tex] such that for some positive integer [tex]n,[/tex]

[tex]nx^3+sinx-2010=0[/tex] and [tex]4ny^3+sinx.cosy+1005=0,[/tex]

then the value of [tex]sin(x+2y)+cos(x+2y)[/tex] is