Numerical Methods for finding the Roots of $f(x)=\sin^2(\frac{33}{x}\pi)+\sin^2(x \pi)$

Question

This question is a continuation of this one; but this time $$f(x)=\sin^2(\frac{33}{x}\pi)+\sin^2(x \pi)$$ Everything about that question holds for this one: I'm looking for numerical root-finding algorithms for this function that approximate the roots fairly accurately. I found that a lot of popular iterative algorithms like Newton's won't work for this function (at least not in this form) as the roots are also minima. And, just like last time, assume I have an interval where only one root must lie in. I am focused on roots $>1$ and $<33$. I picked this equations because the roots can be easily found: $1,3,11,33$. I want to be able to compare the algorithm's accuracy.