Hi

I'm kind of hunting out of my depth relative to my current knowledge so the answer to this might be really obvious - please bear with me ...

I'm trying to find

$\displaystyle \int \frac{1}{sin\theta cos\theta }d\theta $

I've tried integrating the inverse of a function

Inverse Function Integration -- from Wolfram MathWorld

but I ended up with an integral involving

$\displaystyle sin\left (sin\theta cos\theta \right )cos\left (sin\theta cos\theta \right )$

which didn't look very hopeful. It may be because I haven't officially learnt integrating an inverse yet ...

I then tried integration by parts (again something which I had never heard of before), and I changed the original integral to

$\displaystyle \int sec\theta csc\theta \, d\theta $

to do so, but then when it came to chosing which of sec or csc to integrate and which to differentiate, either way seemed to end up with the 'output' integral containing piles of ln, cot, csc, tan all in arrangements I couldn't hope to integrate.

Is there a technique(s) for integrating this which I don't know about yet? Any hints?