If $tanA + cotA = 4$, then $tan^4A + cot^4A$ is equal to

The value of $\theta $ lying between $0$ and $\pi /2$ and satisfying the equation

$\left| {\,\begin{array}{*{20}{c}}{1 + {{\sin }^2}\theta }&{{{\cos }^2}\theta }&{4\sin 4\theta }\\{{{\sin }^2}\theta }&{1 + {{\cos }^2}\theta }&{4\sin 4\theta }\\{{{\sin }^2}\theta }&{{{\cos }^2}\theta }&{1 + 4\sin 4\theta }\end{array}\,} \right| = 0$

The general solution of $\tan 3x = 1$ is

The equation $3{\sin ^2}x + 10\cos x - 6 = 0$ is satisfied, if

The equation $2{\cos ^2}\left( {\frac{x}{2}} \right)\,{\sin ^2}x\, = \,{x^2}\, + \,\frac{1}{{{x^2}}},\,0\,\, \leqslant \,\,x\,\, \leqslant \,\,\frac{\pi }{2}\,\,$ has

The solution set of $(5 + 4\cos \theta )(2\cos \theta + 1) = 0$ in the interval $[0,\,\,2\pi ]$ is