If the slope of one of the lines given by $\mathrm{K} x^2+6 x y+y^2=0$ is three times the order, then the value of $K$ is

$$ \cos ^3\left(\frac{\pi}{8}\right) \cos \left(\frac{3 \pi}{8}\right)+\sin ^3\left(\frac{\pi}{8}\right) \sin \left(\frac{3 \pi}{8}\right)=$$

If $\bar{a}$ and $\bar{b}$ are two unit vectors such that $5 \bar{a}+4 \bar{b}$ and $\bar{a}-2 \bar{b}$ are perpendicular to each other, then the between $\bar{a}$ and $\bar{b}$ is

The value of $\int \frac{\cos ^3 x}{\sin ^2 x+\sin x} \mathrm{~d} x$ is