Domain-parametric equations

Remember, informally, the domain is "what values can x take such that the function f(x) doesn't explode".
So really what it's asking is what values $3\cot^2(2t)$ can it be as t runs through 0 to pi/4.

Or, to make things a bit easier, it's the same as asking $3\cot^2(t)$ as t runs through 0 to pi/2.
The answer should be apparent if you sketch the graph of cot(t).

Remark: It's basically the same as finding the range of the function $f(t)=3\cot^2(2t), 0<t\leq \pi/4$. I just happen to call the function x instead of f. As with finding ranges, I think there are no shortcuts other than sketching the curve first.