If theta is in the interval left(0, frac{pi}{ | vedclass

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(D) Given,$\cos 2 	heta \cdot \sec ^4 	heta + \sec ^2 	heta = 0$ for $	heta \in \left(0, \frac{\pi}{2}ight)$.Since $\sec 	heta 
eq 0$,we can d

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$\frac{2}{3}$

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(D) Given,$\cos 2 	heta \cdot \sec ^4 	heta + \sec ^2 	heta = 0$ for $	heta \in \left(0, \frac{\pi}{2}ight)$.Since $\sec 	heta 
eq 0$,we can divide by $\sec ^2 	heta$:$\cos 2 	heta \cdot \sec ^2 	heta + 1 = 0$Using the identity $\cos 2 	heta = \frac{1 - 	an ^2 	heta}{1 + 	an ^2 	heta}$ and $\sec ^2 	heta = 1 + 	an ^2 	heta$:$\left(\frac{1 - 	an ^2 	heta}{1 + 	an ^2 	heta}ight) (1 + 	an ^2 	heta) + 1 = 0$$1 - 	an ^2 	heta + 1 = 0$$2 - 	an ^2 	heta = 0$$	an ^2 	heta = 2$Since $	an ^2 	heta = \frac{\sin ^2 	heta}{\cos ^2 	heta} = \frac{\sin ^2 	heta}{1 - \sin ^2 	heta} = 2$,we have:$\sin ^2 	heta = 2 - 2 \sin ^2 	heta$$3 \sin ^2 	heta = 2$$\sin ^2 	heta = \frac{2}{3}$

If $\theta$ is in the interval $\left(0, \frac{\pi}{2}\right)$ satisfying the equation $\cos 2 \theta \cdot \sec ^4 \theta + \sec ^2 \theta = 0$,then $\sin ^2 \theta =$

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