Evaluate:
$\frac{\sin ^{2} 63^{\circ}+\sin ^{2} 27^{\circ}}{\cos ^{2} 17^{\circ}+\cos ^{2} 73^{\circ}}$

State whether the following is true or false. Justify your answer.
$\cot A$ is not defined for $A = 0^{\circ}$.

$\frac{\sin 60^{\circ} + \cos 30^{\circ}}{1 + \sin 30^{\circ} + \cos 60^{\circ}} = \dots$

$2 \sin ^{2} 30^{\circ} \cot 30^{\circ}-3 \cos ^{2} 60^{\circ} \sec ^{2} 30^{\circ} = \dots$

In a right triangle,if the measure of one of the angles is $60^{\circ}$,then the measure of the side opposite to the angle with measure $60^{\circ}$ is $\ldots \ldots$ times the measure of the hypotenuse.

If $\tan \theta = \sqrt{3}$,then $\theta = \ldots$ (in $^\circ$)