If `|[1+sin^2theta, cos^2 theta,4sin 2theta] , [sin^2theta, 1+cos^2theta,4sin2theta] , [sin^2theta,cos^2theta,4sin2theta-1]|=0` and `0 lt theta lt pi/2` then `cos4theta=`

If |(1+sin^(2)theta, cos^(2)theta, 4 sin 2 theta),(sin^(2) theta, 1+cos^(2)theta, 4sin2 theta),(sin^(2)theta, cos^(2)theta, 4 sin 2 theta-1)|=0 and 0 lt theta lt (pi)/2 then cos 4 theta=

If |[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 , then the value of theta is

The value of theta lying between 0 and 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 (A) (7pi)/24 or (11pi)/24 (B) (5pi)/24 (C) pi/24 (D) none

1+sin^(2)theta,sin^(2)theta,sin^(2)thetacos^(2)theta,1+cos^(2)theta,cos^(2)theta4sin4 theta,4sin4 theta,1+4sin4 theta]|=0

sin^2theta+cos^4theta=cos^2theta+sin^4theta

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 =

If |(1+sin^2 theta,sin^2 theta,sin^2 theta),(cos^2 theta,1+cos^2 theta,cos^2 theta),(4sin 4 theta,4sin4theta,1+4sin4theta)|=0, then ... sin 4theta equal to ....