If `|{:(1+cos^(2)theta,sin^(2)theta,4cos6theta),(cos^(2)theta,1+sin^(2)theta,4cos6theta),(cos^(2)theta,sin^(2)theta,1+4cos6theta):}|=0`, and `theta in (0,(pi)/(2))`, then value of `theta` is

If |{:(1+cos^(2)theta,sin^(2)theta,4cos6theta),(cos^(2)theta,1+sin^(2)theta,4cos6theta),(cos^(2)theta,sin^(2)theta,1+4cos6theta):}|=0 , and theta in (0,(pi)/(3)) , then value of theta is

If |{:(1+cos^(2)theta,sin^(2)theta,4cos6theta),(cos^(2)theta,1+sin^(2)theta,4cos6theta),(cos^(2)theta,sin^(2)theta,1+4cos6theta):}|=0 , and theta in (0,(pi)/(3)) , then value of theta is

If |{:(1+cos^(2)theta,sin^(2)theta,4cos6theta),(cos^(2)theta,1+sin^(2)theta,4cos6theta),(cos^(2)theta,sin^(2)theta,1+4cos6theta):}|=0 , and theta in (0,(pi)/(3)) , then value of theta is

sin^(6)theta+cos^(6)theta+3sin^(2)theta cos^(2)theta=1

cos^(3)2 theta+3cos2 theta=4(cos^(6)theta-sin^(6)theta)

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

A value of theta in (0, pi//3), for which |{:(1+"cos"^(2)theta, "sin"^(2)theta, 4"cos" 6 theta), ("cos"^(2)theta, 1+"sin"^(2)theta, 4"cos"6theta), ("cos"^(2)theta, "sin"^(2)theta, 1+4"cos"6theta):}| = 0, is

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