$\frac{1}{\cos ^{2} \theta}-\frac{1}{\cot ^{2} \theta} = \dots$

If $\sec 4A = \operatorname{cosec}(A - 20^{\circ})$,where $4A$ is an acute angle,find the value of $A$ (in $^{\circ}$).

The value of $\tan 5^{\circ} \cdot \tan 25^{\circ} \cdot \tan 45^{\circ} \cdot \tan 65^{\circ} \cdot \tan 85^{\circ}$ is $\ldots \ldots \ldots \ldots .$.

$\frac{\sec \theta-1}{\sec \theta+1} = \ldots$

The value of the expression $\left[\frac{\sin ^{2} 22^{\circ}+\sin ^{2} 68^{\circ}}{\cos ^{2} 22^{\circ}+\cos ^{2} 68^{\circ}}+\sin ^{2} 63^{\circ}+\cos 63^{\circ} \sin 27^{\circ}\right]$ is:

$\cos \theta = \frac{b}{\sqrt{a^2 + b^2}}$; where,$0 < \theta < 90^\circ$; then $\sin \theta = \dots$