I'm so bad at trig

Geometry Level pending

Let there be 2 acute angles, \(\theta\) and \(\beta\) which satisfy the relation \(a \sec \theta + b\sec \beta = c\), where \(a,b,c\) are positive integers. Given that \(\theta = 72\), find the value of \(\beta\) that minimizes the expression \(a \cos(72) + b\cos\beta\).

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