Solve (sin(3x)-sin(x))(cos(3x+cos(x))

$$( \sin ( 3x ) - \sin ( x ) )( \cos ( 3x+ \cos ( x ) )$$

Evaluate

$$\sin(x)\left(3\left(\cos(x)\right)^{2}-\left(\sin(x)\right)^{2}-1\right)\left(\cos(x)\cos(\cos(x))\left(\left(\cos(x)\right)^{2}-3\left(\sin(x)\right)^{2}\right)-\sin(x)\sin(\cos(x))\left(3\left(\cos(x)\right)^{2}-\left(\sin(x)\right)^{2}\right)\right)$$

Differentiate w.r.t. x

$$\frac{\sin(x)\left(3\left(\cos(x)\right)^{2}-\left(\sin(x)\right)^{2}-1\right)\left(4\sin(x)\sin(\cos(x))\left(\cos(x)\right)^{3}-12\cos(x)\sin(\cos(x))\left(\sin(x)\right)^{3}-4\cos(\cos(x))\left(\sin(x)\right)^{4}+36\cos(x)\sin(\cos(x))\left(\sin(x)\right)^{2}-36\sin(x)\cos(\cos(x))\left(\cos(x)\right)^{2}+12\cos(\cos(x))\left(\sin(x)\right)^{3}-12\sin(\cos(x))\left(\cos(x)\right)^{3}+3\cos(\cos(x))\left(\sin(2x)\right)^{2}\right)+4\cos(x)\left(3\left(\cos(x)\right)^{2}-\left(\sin(x)\right)^{2}-1\right)\left(\cos(x)\cos(\cos(x))\left(\left(\cos(x)\right)^{2}-3\left(\sin(x)\right)^{2}\right)-\sin(x)\sin(\cos(x))\left(3\left(\cos(x)\right)^{2}-\left(\sin(x)\right)^{2}\right)\right)-32\cos(x)\left(\sin(x)\right)^{2}\left(\cos(x)\cos(\cos(x))\left(\left(\cos(x)\right)^{2}-3\left(\sin(x)\right)^{2}\right)-\sin(x)\sin(\cos(x))\left(3\left(\cos(x)\right)^{2}-\left(\sin(x)\right)^{2}\right)\right)}{4}$$