Could anyone help me with this? I'm stuck.

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> If $$(1 + \operatorname{cis}x)(1 + \operatorname{cis} 2x) = a + bi$$ prove that $$a^2 + b^2 = \left(4\cos x \cos\frac x2\right)^2$$
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For reference, $\operatorname{cis}x = \cos x + i\sin x$.

I found that 
$$a = 1 + \cos x + \cos2x + \cos3x \quad\text{and}\quad 
b = \sin x + \sin2x + \sin3x$$