If $\tan 2A = \cot(A - 18^{\circ})$,where $2A$ is an acute angle,find the value of $A$ (in $^{\circ}$).

Evaluate the following:
$2 \tan ^{2} 45^{\circ}+\cos ^{2} 30^{\circ}-\sin ^{2} 60^{\circ}$

Evaluate the following:
$\frac{5 \cos ^{2} 60^{\circ}+4 \sec ^{2} 30^{\circ}-\tan ^{2} 45^{\circ}}{\sin ^{2} 30^{\circ}+\cos ^{2} 30^{\circ}}$ (in $/12$)

If $\operatorname{cosec} \theta = \sqrt{2}$,then the value of $\tan \theta$ is:

If $\operatorname{cosec} \theta = \frac{2}{\sqrt{3}}$,then $\theta = \ldots$ (in $^\circ$)

In a right triangle,if the measure of one of the angles is $45^{\circ}$,then the measure of the side opposite to the angle with measure $45^{\circ}$ is $\ldots \ldots \ldots$ times the measure of the hypotenuse.