[p=(1)/(2)sin^(2)theta+(1)/(3)cos^(2)theta,quad " then "],[(1)/(3)<=p<=(1)/(2)],[" O ">=2],[" 0"<=p<=3],[qquad (-sqrt(13))/(6)<=P<=(sqrt(13))/(6)]

If P=(1)/(2)sin^(2)theta+(1)/(3)cos^(2)theta , then

If P=(1)/(2)sin^(2)theta+(1)/(3)cos^(2)theta then

If P = 1/2 sin^(2)theta + 1/3 cos^(2)theta , then

P=1/2 sin^2 theta+1/3 cos^2 theta , then :

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

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+sin^(2)theta = 3 sin theta cos theta , then theta =