The Tetrahedron Problem

$\vec{a},\vec{b}$ and $\vec{c}$ are three non coplanar unit vectors inclined at an angle $\alpha (\leq \dfrac{\pi}{2} )$ to each other . If volume of the tetrahedron formed by these vectors is $\dfrac{1}{\sqrt{360}}$ . Then find the value of

$3{\cos}^{2} \alpha -2\cos^{3} \alpha.$