[tex]{{a}_{n}}=\left| \sin \left( \pi \sqrt[3]{{{n}^{3}}+{{n}^{2}}} \right) \right|=\left| \sin \left( n\pi -\pi \sqrt[3]{{{n}^{3}}+{{n}^{2}}} \right) \right|=\left| \sin \left( n-\sqrt[3]{{{n}^{3}}+{{n}^{2}}} \right)\pi \right|=\\=\left| \sin \frac{{{n}^{2}}\pi }{\sqrt[3]{{{n}^{6}}}+\sqrt[3]{{{n}^{3}}({{n}^{3}}+{{n}^{2}})}+\sqrt[3]{{{({{n}^{3}}+{{n}^{2}})}^{2}}}} \right|\to \left| \sin \frac{\pi }{3} \right|=\frac{\sqrt{3}}{2}[/tex]