Number of values of `theta` lying between `theta=0 and theta=pi` satisfying the equation `|(1 +sin^2 theta,cos^2 theta,4 sin 6 theta),(sin^2 theta,1+cos^2 theta,4 sin 6 theta),(sin ^2 theta,cos^2 theta,1+4sin 6 theta)|=0` is

The value of theta lying between theta =0 and theta=(pi)/2 and satifying the equation |{:(1+sin^2theta,cos^2theta,4sin4theta),(sin^2theta,1+cos^2theta,4sin4theta),(sin^2theta,cos^2theta,1+4sin4theta):}|=0 is then theta =

The value of theta lying between theta=0 and theta=pi/2 and satisfying the equation |[1+sin^2theta,cos^2theta,4sin4theta],[sin^2theta,1+cos^2theta,4sin4theta],[sin^2theta,cos^2theta,1+4sin4theta]|=0 are

The value of theta lying between theta = 0 and theta = pi//2 and satisfying the equation |(1+sin^(2)theta,cos^(2)theta,4sin4theta),(sin^(2)theta,1+cos^(2)theta,4sin4theta),(sin^(2)theta,cos^(2)theta,1+4sin4theta)|=0 are a) 3pi//24 b) 5pi//24 c) 11pi//24 d) pi//24

The value of theta , lying between theta =0 and theta=(pi)/(2) and satisfying the equation . |{:(1+ cos^(2 ) theta , sin^(2) theta , 4 sin 4 theta ),(cos^(2) theta , 1+sin^2 theta , 4 sin 4 theta ),(cos^(2) theta , sin^(2) theta , 1+ 4 sin 4 theta ):}|=0 , is