Does this erratically-behaved infinite sum converge?

Question

I have been trying to find the convergence (and value) of this infinite sum: $$\sum_{n=1}^\infty \frac{\sin(n)^n}{\cos(en)}$$ The partial sums behave relatively unpredictably and at some point become very hard to evaluate because of the exponent on the $\sin$, but from what I've seen I can't tell if it converges or not, although since the top is raised to the power $n$ it feels like it should. I tried the ratio test but that really doesn't lead anywhere, and applying L'Hôpital's rule doesn't help evaluate the limit. WolframAlpha can't give any useful info about the sum or its convergence either.