How to prove this inequality about trigonometric polynomial？

Question

Problem statement:
Define $T_n(x)=\frac{a_0}{2}+\sum_{k=1}^{n}{(a_k\cos kx+b_k\sin kx)}$ be a real valued trigonometric polynomial on $[-\pi,\pi]$.
Prove that $$\mathop{max}\limits_{-\pi\le x \le \pi}{|{T_n}'(x) |}\le n^2\mathop{max}\limits_{-\pi\le x \le \pi}{|{T_n}(x) |}$$ It seems difficult to calculate the maximum of a trigonometric polynomial. And I find it hard to establish a connection between two maximum values. How to prove this inequality? I would appreciate if you can give some help.