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Calculus Level 5

\[ \large \int_0^\pi \cos^{14} \theta \, d\theta = \dfrac{A+B\pi}C \]

If the equation above holds true for integers \(A,B\) and \(C\) with \(C\) is positive and minimized, find \( (A+B+C) \bmod{100} \).


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