$-1\le \sin(x+\dfrac{\pi}{3})\le 1$
$\Rightarrow -215\le -215\sin(x+\dfrac{\pi}{3})\le 215$
$-1\le \sin(x+\dfrac{\pi}{4})\le 1$
$\Rightarrow -204\le 204\sin(x+\dfrac{\pi}{4})\le 204$
$\Rightarrow -215-204\le y\le 215+204$
$\Leftrightarrow -419\le y\le 419$
$\to \min y=-419; \max y=419$