Answer
$$y'=-3\sin(\sin3\theta)\cos3\theta$$
$$y''=-9\cos(\sin3\theta)\cos^23\theta+9\sin(\sin3\theta)\sin3\theta$$
Work Step by Step
$$y'=(\cos(\sin3\theta))'=-\sin(\sin3\theta)\cdot(\sin3\theta)'=
-\sin(\sin3\theta)\cos3\theta\cdot(3\theta)'=
-\sin(\sin3\theta)\cos3\theta\cdot3=
-3\sin(\sin3\theta)\cos3\theta$$
$$y''=(y')'=(-3\sin(\sin3\theta)\cos3\theta)'=
(-3\sin(\sin3\theta))'\cos3\theta-3\sin(\sin3\theta)(\cos3\theta)'=
-3\cos(\sin3\theta)\cdot(\sin3\theta)'\cos3\theta-3\sin(\sin3\theta)(-\sin3\theta)\cdot(3\theta)'=
-3\cos(\sin3\theta)\cos3\theta(3\theta)'\cos3\theta+3\sin(\sin3\theta)\sin3\theta\cdot3=
-3\cos(\sin3\theta)\cos^23\theta\cdot3+9\sin(\sin3\theta)\sin3\theta=-9\cos(\sin3\theta)\cos^23\theta+9\sin(\sin3\theta)\sin3\theta$$