sin^(2)theta+cos^(4)theta

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

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

Prove that sin^(4)theta+2sin^(2)thetacos^(2)theta+cos^(4)theta=1

The sum of all values of theta in (0,pi/2) satisfying sin^(2)2theta+cos^(4)2theta=3/4 is

The sum of all values of theta in (0,pi/2) satisfying sin^(2)2theta+cos^(4)2theta=3/4 is

2(1-2sin^(2)theta)cos4 theta=