quiz about local minimum and maximum

Question

I am student learning calculus, and have got stuck on one of calculus quiz

the quiz gives the equation, $\frac{\mathrm{d}y}{\mathrm{d}x} = x\sin{x}-\cos{x}$ for $0<x<4$

and ask for $x$ location of local maximum.

so my solution process was to find out $\frac{\mathrm{d}y}{\mathrm{d}x}=0$, so that

1. $x\sin{x}=\cos x$
2. $\tan{x}=\frac{1}{x}$
3. $\arctan{\frac{1}{x}} = x$
4. derivative both side
5. It turns out $x^2 = -2$.

I guess making simple mistakes here, which i can't find out would be grateful if someone can help me out.