If the equation $tan^4x -2sec^2x + [a]^2 = 0$ has atleast one solution, then the complete range of $'a'$ (where $a \in R$ ) is 
(Note : $[k]$ denotes greatest integer less than or equal to $k$ )

The solution of the equation $4{\cos ^2}x + 6$${\sin ^2}x = 5$

Number of solutions to the system of equations $sin \frac{x+y}{2}=0$ and $|x| + |y| = 1$

The number of solution of the equation $\tan x + \sec x = 2\cos x$ lying in the interval $(0,2\pi )$ is

The solution set of the equation $tan(\pi\, tanx) = cot(\pi\, cot\, x)$ is

The number of all possible values of $\theta$, where $0<\theta<\pi$, for which the system of equations

$ (y+z) \cos 3 \theta=(x y z) \sin 3 \theta $

$ x \sin 3 \theta=\frac{2 \cos 3 \theta}{y}+\frac{2 \sin 3 \theta}{z} $

$ (x y z) \sin 3 \theta=(y+2 z) \cos 3 \theta+y \sin 3 \theta$ have a solution $\left(\mathrm{x}_0, \mathrm{y}_0, \mathrm{z}_0\right)$ with $\mathrm{y}_0 \mathrm{z}_0 \neq 0$, is