Ok, first, get rid of the square brackets. In Maple, these define a list. You do not have a list here.
Second, I suggest you use 1-d input when you actually do work in Maple (as opposed to typesetting something). As it is; your worksheet appears to use theta as well as theta(t). I am not quite certain whether 2-d input keeps track of the arguments (i.e. always takes theta as theta(t)) but I suspect it is not. At any rate, it is confusing.
Redefining sin(theta) and/or cos(theta) the way you do it does not seem to me the way to go. In particular it may mess up your differentials sin(diff(theta(t),t)) Instead, I would do what the small angle approximation in reality is: work with the first-order approximation. Maple has the handy series command for that: e.g.
and if you wrap it in a convert statement you get a normal polynomial expression:
Now you do have another problem in that series will not work on functions. To make this work you can use freeze/thaw. In brief, if you substitute an expression with freeze(expression) it will take it as atomic but keep track of what it is so when you thaw later on it'll put the original back in.
Your calculation then becomes the following:
thdoubledot:=solve(de,[diff(theta(t),t,t)]); # the two  get rid of the list-creating brackets
where the last two should be in one execution group to avoid problems with the % operator.
In this way you are still left with the sine and cosine of diff(theta(t),t). It is up to you to decide whether you can linearize that or not, and what the corrrect way to do this linearization is (correct for your problem, not for Maple).
So, it is a bit messier than one would like, but along these lines you should be able to get where you need to go. Maybe someone else knows a better way??
Edit: Fixed two typos.