How to integrate $\int \frac{1}{\sin^4(x)\cos^4(x)}\,\mathrm dx$? How can I integrate $$\int \frac{1}{\sin^4(x)\cos^4(x)}\,\mathrm dx.$$
So I know that for this one we have to use a trigonometric identity or a substitution. Integration by parts is probably not going to help. Can someone please point out what should I do to evaluate this integral?  
Thanks!

\begin{align*}
\int \frac{16}{16 \sin^4(x)\cos^4(x)}dx  &= 16 \int \frac{1}{(2 \sin(x)\cos(x))^4} dx \\
&= 16 \int \csc^4(2x)dx \\  
& = 16 \int \csc^2(2x) \csc^2(2x)dx\\ 
&= 16 \int  (1 + \cot^2(2x)) \csc^2(2x) dx \\ 
&= 16 \int \csc^2(2x)dx + 16 \int  \cot^2(2x)\csc^2(2x)dx \\  
&= \; \;\dots \\
&= \; \; \dots \\
\end{align*}
For the last let, $\cot(2x) = u$
