This looks brutal. The only way I can see to do it is to expand the top and bottom as power series. To do this for the numerator, use the series

and . Then

(plus powers higher than 7), with a similar expression for . When you subtract these, I think that the lowest surviving power of x in will be something like .

Now do the same thing for the denominator, using the power series for the inverse trig functions, and presumably the lowest surviving power of x will again be some multiple of . I don't have the stamina to check that.