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  4. The value of θ lying between θ=0 θ=π / 2 satisfying the equation: | 1+ sin 2 θ cos 2 θ 4 sin 4 θ sin 2 θ 1+ cos 2 θ 4 sin 4 θ sin 2 θ cos 2 θ 1+4 sin 4 θ |=0 text are:

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Q. The value of $\theta$ lying between $\theta=0 \& \theta=\pi / 2 \&$ satisfying the equation : $\begin{vmatrix} 1+\sin ^2 \theta & \cos ^2 \theta & 4 \sin 4 \theta \\ \sin ^2 \theta & 1+\cos ^2 \theta & 4 \sin 4 \theta \\ \sin ^2 \theta & \cos ^2 \theta & 1+4 \sin 4 \theta \end{vmatrix}=0 \text { are : }$

Determinants

Solution:

$R _1 \rightarrow 2 R _1- R _2$ and $R _2 \rightarrow R _2- R _3$