Example of a system in $L^2[-\pi,\pi]$ which is complete, but not orthogonal

Question

An example of system in $L^2[-\pi,\pi]$ which is orthogonal, but not complete could be the system of functions $\{x^{2k+1}, k=0,1,2,3,...\}$.

But I can't think of a system in $L^2[-\pi,\pi]$ that is complete but not orthogonal. Could someone give me an example?