Without using trigonometric tables, find the value of each of the expressions given below: \[ \l...

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Without using trigonometric tables, find the value of each of the expressions given below:
\[
\left\{\frac{\sin ^{2} 22^{\circ}+\sin ^{2} 68^{\circ}}{\cos ^{2} 22^{\circ}+\cos ^{2} 68^{\circ}}+\sin ^{2} 63^{\circ}+\cos 63^{\circ} \sin 27^{\circ}\right\}
\]
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