Solve (x^{3}-15 x-4=0) using the method for solving cubics. Now cleverly spot an integer root. Deduce that [ cos left(frac{1}{3} tan ^{-1}left(frac{11}{2} ight) ight)=frac{2}{sqrt{5}} ]

Solve \(x^{3}-15 x-4=0\) using the method for solving cubics.

Now cleverly spot an integer root. Deduce that

\[ \cos \left(\frac{1}{3} \tan ^{-1}\left(\frac{11}{2}\right)\right)=\frac{2}{\sqrt{5}} \]