How to calculate this integral in one variable I want calculate this integral
$$ \int_0^{2\pi} - \frac{\cos t \; ( 2 (\sin t)^2 + (\cos t)^2)}{(\cos t)^4 + (\sin t)^2} \, dt $$
Can I use an opportunity substitution?

HINT: Consider $\int_{-\pi/2}^{\pi/2} f(t)\,dt + \int_{\pi/2}^{3\pi/2} f(t)\,dt$. In particular, what is $f(t+\pi)$ compared to $f(t)$?
