\left(\left(\sqrt{3}\mbox{tg} \hspace{2pt} u\right)^2+3\right)^2=\left(3\mbox{tg}^2u+3\right)^2=9\left(\frac{\sin ^2 u+\cos ^2u}{\cos ^2u}\right)^2=9 \frac{1}{\cos ^4u}=9 \sec ^4u