Simplify \(\left(\sec\theta - \frac{1}{\sec\theta}\right) \times \left(\text{cosec}\theta - \frac{1}{\text{cosec}\theta}\right) \times \left(\sin\theta - \frac{1}{\sin\theta}\right).\)
\( \cos ^{3}\theta \)
\( -\sin ^{3}\theta \)
\( \sin ^{3}\theta \)
\( -\cos ^{3}\theta \)
If \( a^{2} + b^{2} = 168 \), a × b = 27, and a > b, find \(\frac{a-b}{a+b}\).
\(\sqrt{\frac{57}{111}}\)
\(\sqrt{\frac{53}{121}}\)
\(\frac{57}{111}\)
\(\frac{55}{121}\)