The solution of the equation \(\left| {\begin{array}{*{20}{c}} {1 + {{\sin }^2}x}&{{{\sin }^2}x}&{{{\sin }^2}x}\\ {{{\cos }^2}x}&{1 + {{\cos }^2}x}&{{{\cos }^2}x}\\ {4\sin 2x}&{4\sin 2x}&{1 + 4\sin 2x} \end{array}} \right| = 0,\left( {0 < x < \pi } \right)\) are :
1
\(\frac{\pi}{6},\frac{5\pi}{6}\)
2
\(\frac{5\pi}{12},\frac{7\pi}{12}\)
3
\(\frac{7\pi}{12},\frac{11\pi}{12}\)
4
\(\frac{\pi}{12},\frac{\pi}{6}\)