Mathematics

This problem tests whether you can evaluate basic trig values and then handle a product of differences. The key insight is that $\csc$ and $\sec$ are reciprocals of $\sin$ and $\cos$—so each difference becomes a fraction minus its reciprocal. Once you substitute the exact values at $\frac{\pi}{6}$ (which you should memorize), the arithmetic simplifies cleanly if you find a common denominator within each parenthesis.

This problem tests whether you can evaluate basic trig values and then handle a product of differences. The key insight is that $\csc$ and $\sec$ are reciprocals of $\sin$ and $\cos$—so each difference becomes a fraction minus its reciprocal. Once you substitute the exact values at $\frac{\pi}{6}$ (which you should memorize), the arithmetic simplifies cleanly if you find a common denominator within each parenthesis.