[填空题]
1. Given that $\theta=18^{\circ}$ satisfies the equation $4 \sin ^{2} \theta+2 \sin \theta-1=0$ , find the value of $\sin 18^{\circ}$ .
2. Hence find the value of $\cos 36^{\circ}$ .
The following diagram shows the triangle ABC where $ \mathrm{AB}=4 \mathrm{~cm}, \mathrm{BC}=5 \mathrm{~cm}$ and $\mathrm{CBA}=36^{\circ}$ .
$\text { 3. Find } \mathrm{AC} \text { in the form } \sqrt{a+b \sqrt{5}} \mathrm{~cm} \text { where } a, b \in \mathbb{Z} \text {. }$
