The general solution of the equation $\tan x+\tan 2 x-\tan 3 x=0$ is

Number of solutions of the trigonometric equation $2 \tan 2 \theta-\cot 2 \theta+1=0$ lying in the interval $[0, \pi]$ is

For $a \in R-\{0\}$, if $a \cos x+a \sin x+a=2 k+1$ has a solution, then $k$ lies in the interval

If the general solution .set of $\sin x+3 \sin 3 x+\sin 5 x=1$ is $S$, then $\{\sin \alpha / \alpha \in S\}=$