Infinite Series Sum Question Help Please?

For each of the following two series, determine whether it is absolutely convergent, conditionally convergent or divergent. Justify your answers. (-1)^n * Tan^2(1/x^1/3) Now I started of by removing the -1 to prove absolute convergence. I used the direct comparison to prove divergence since 1/x^2/3 < Tan^2(x^1/3) I hope the above is right, please correct me if I am wrong. I then moved on to consider it with the -1^n and tryed the alternating series test. The first condition is met since the limit does approach zero but I'm baffled if the second is met where it is a decreasing function? Please help me out with this and point out any flaws in my logic that you can find.