Cos the limit is funny

Calculus Level 3

\[\begin{eqnarray} f(x) &=& \dfrac{1-\cos(1-\cos x)}{x^4} , x \neq 0 \\ f(0) &=& a \end{eqnarray} \]

The function \(f(x)\) is defined as above. If \(f(x)\) is continuous everywhere, then \(a\) is equal to \(\dfrac{A}{B}\) for coprime positive integers \(A\) and \(B\), find \(A+B\).

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