In a regular tetrahedron, let θ be the angle between any edge and a face not containing the edge. If cos2θ=ab where a,b∈I+ also a and b are co-prime, then the value of 513(10a+b)= ___

Use angle between line, plane concept, cosθ=13

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In a regular tetrahedron, let $θ$ be the angle between any edge and a face not containing the edge. If $\cos^{2} θ = \frac{a}{b}$ where $a, b \in I^{+}$ also a and b are co-prime, then the value of $\frac{5}{13} (10 a + b) =$ ___

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answer is 5.

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Use angle between line, plane concept, $\cos θ = \frac{1}{\sqrt{3}}$

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