$$2 \sin \left(\theta+\frac{\pi}{3}\right)=\cos \left(\theta-\frac{\pi}{6}\right)$$, then $$\tan \theta=$$

$$\int[1+2 \tan x(\tan x+\sec x)]^{\frac{1}{2}} d x= $$

The general solution of the differential equation $$\left(3 x y+y^2\right) d x+\left(x^2+x y\right) d y=0$$ is

In a meeting $$60 \%$$ of the members favour and $$40 \%$$ oppose a certain proposal. A member is selected at random and we take $$\mathrm{X}=0$$ if he opposed and $$\mathrm{X}=1$$ if he is in favour, then $$\operatorname{Var} \mathrm{X}=$$