Questions in trigonometry

Select	Question
	If $4{{\sin }^{4}}x+{{\cos }^{4}}x=1,$then $x =$
	If $\cos 3x+\sin \left( 2x-\frac{7\pi }{6} \right)=-2$, then $x=$ (where $k\in Z$)
	The solution of the equation $\begin{vmatrix} {\cos \theta } & {\sin \theta }&{\cos \theta }\\ { - \sin \theta }&{\cos \theta }&{\sin \theta }\\ { - \cos \theta }&{ - \sin \theta }&{\cos \theta } \end{vmatrix} = 0$ , is
	The set of values of x for which the expression $\frac{\tan 3x-\tan 2x}{1+\tan 3x\tan 2x}=1$, is
	If $\tan \theta +\tan 2\theta +\sqrt{3}\tan \theta \tan 2\theta =\sqrt{3},$then
	The roots of the equation $1-\cos \theta =\sin \theta .\sin \frac{\theta }{2}$ is
	If $\frac{\tan 3\theta -1}{\tan 3\theta +1}=\sqrt{3}$, then the general value of $\theta $is
	If $2{{\cos }^{2}}x+3\sin x-3=0,\,\,0\le x\le {{180}^{o}}$, then $x =$
	The equation $\sin x+\cos x=2$has
	The number of values of $\theta $ in $[0, 2\pi ]$ satisfying the equation $2{{\sin }^{2}}\theta =4+3 \cos \theta $ are