Angles of a triangles whose $2$ sides are given by $2$ vectors

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Let $\hat{a}$ be a unit vector and $\vec{b}$ be a non zero vector

not parallel to $\hat{a}\; $.Find the angles of a triangle,

two sides of which are represented by the vectors

$\sqrt{3}(\hat{a}\times \vec{b})$ and $\vec{b}-(\hat{a}\cdot \vec{b})\hat{a}.$

Try: Let $\vec{p}=\sqrt{3}(\hat{a}\times \vec{b})$ and $\vec{q}=\vec{b}-(\hat{a}\cdot \vec{b})\hat{a}$

So $\vec{q}=(\hat{a}\cdot \hat{a})\vec{b}-(\hat{a}\cdot \vec{b})\hat{a}=-\hat{a}\times (\hat{a}\times \vec{b})$

did not know how do i solve it , could some help me , Thanks