The tick labels can be accessed via the get_text method of the class <class 'matplotlib.axes.AxesSubplot'>, i.e. the ax object of our example.
A value for a tick can be changed with the set_bbox method.
Getting all the tick labels:
labels = [xtick.get_text() for xtick in ax.get_xticklabels()]
If print(labels) is applied, we see the following output:
['$-2\\pi$', '$-\\pi$', '$+\\pi$', '$+2\\pi$']
We can adjust all the labels now by indexing labels:
Labels[1] = '42'
This resets sets the new tick labels:
ax.set_xticklabels(labels)