Trig. neravenstva

[sasa]

Let $ {\mathbf a} : =\displaystyle 2\cdot \cos{\frac{\pi}{7}} $ and $ A,{\mathbf B} , C, D $ such that
$ 1 + {\mathbf a} \cos{x}+A\cos{2x}+{\mathbf B} \cos{3x}+C\cos{4x}+D\cos{5x} \ge 0\; \; \; ,\; \; \; \; \; \forall x \in [0,\pi] . $ Find $ {\mathbf B} $ .