[1+sin^(2)theta,cos^(2)theta,4sin4 theta],[sin^(2)theta,1+cos^(2)theta,4sin4 theta],[sin^(2)theta,cos^(2)theta,1+4sin4 theta],[" iber of solutions of "f(theta),=0" in "]

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

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^(4)theta+cos^(4)theta=1-2sin^(2)theta cos^(2)theta

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 0 and (pi)/(2), and satisfying ,,1+sin^(2)theta,cos^(2)theta,4sin4 thetasin^(2)theta,1+cos^(2)theta,4sin4 thetasin^(2)theta,cos^(2)theta,1+4sin4 theta]|=0

sec^(2)theta-(sin^(2)theta-2sin^(4)theta)/(2cos^(4)theta-cos^(2)theta)=1