How to evaluate $\lim\limits_{x\to0}\frac{\tan(x)\cdot\arctan(x)-x^2}{x^6}$

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Find $\;\lim\limits_{x\to0}\dfrac{\tan(x)\cdot\arctan(x)-x^2}{x^6}$

I've recently learnt about L'Hôpital's rule. When I apply it repeatedly here it seems to get complex fast, so wondered if there was a better way to solve it. Thanks in advance.