Let $\mathbf{a},$ $\mathbf{b},$ and $\mathbf{c}$ be three unit vectors, such that the angle between any of them is the acute angle $\theta.$  The volume of the tetrahedron generated by these three vectors is $\frac{1}{\sqrt{360}}.$  Find
\[3 \cos^2 \theta - 2 \cos^3 \theta.\]
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Let $\mathbf{a},$ $\mathbf{b},$ and $\mathbf{c}$ be three unit vectors, such that the angle between any of them is the acute angle $\theta.$  The volume of the tetrahedron generated by these three vectors is $\frac{1}{\sqrt{360}}.$  Find
\[3 \cos^2 \theta - 2 \cos^3 \theta.\]
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\frac{9}{10}
Let $\mathbf{a},$ $\mathbf{b},$ and $\mathbf{c}$ be three unit vectors, such that the angle between any of them is the acute angle $\theta.$  The volume of the tetrahedron generated by these three vectors is $\frac{1}{\sqrt{360}}.$  Find
\[3 \cos^2 \theta - 2 \cos^3 \theta.\]
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