PROBLEM:$\displaystyle \lim_{x\to\(\pi^+)}{(1+3sinx)^{cot(x)}}$

ATTEMPT:

Does L'Hopital's Rule apply work for this problem? I don't think so, because it is not in the appropriate indeterminate form; for, it would be $\displaystyle 1^\infty$. But I don't know any elementary methods that would be appropriate here, nor any limit properties. :/