本题目来源于试卷: Complex Numbers，类别为 IB数学
[问答题]
1. Solve $ 2 \sin \left(x+120^{\circ}\right)=\sqrt{3} \cos \left(x+60^{\circ}\right)$, for $x \in\left[0,180^{\circ}\right]$ .
2. Show that $\sin 75^{\circ}+\cos 75^{\circ}=\frac{\sqrt{6}}{2}$ .
3. Let $z=\sin 4 \theta+\mathrm{i}(1-\cos 4 \theta)$ , for $z \in \mathbb{C}$, $\theta \in\left[0,90^{\circ}\right]$ .
1. Find the modulus and argument of z in terms of $\theta$ .
2. Hence find the fourth roots of z in modulus-argument form.
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