$\lim_{x\to 0} \frac{1-\cos (1-\cos (1-\cos x))}{x^{a}}$ is finite then the max value of $a$ is? I know the formula $\frac{1-\cos x}{x^{2}}=\dfrac{1}2$
But how do i use it here and tried l hospital and no use and doing l hospital twice will make it very lengthy how do i approach ?

Hint. 
$$ \frac{1 - \cos\bigl(1 - \cos(1-\cos x)\bigr)}{x^a} 
 = \frac{1 - \cos\bigl(1 - \cos(1-\cos x)\bigr)}{\bigl(1 - \cos(1 - \cos x)\bigr)^2} \cdot \left(\frac{1 - \cos(1 - \cos x)}{(1 - \cos x)^2}\right)^2 \cdot \frac{(1 - \cos x)^4}{x^a} $$
