This problem involves evaluating a definite integral of trigonometric functions. The key strategy for such integrals is often to manipulate the integrand into a form suitable for a standard substitution, typically involving $\tan x$ or $\cot x$.

1. Key Concept: Transforming Trigonometric Integrals for Substitution

When faced with integrals involving products of powers of $\sec x$ and $\csc x$ (or $\sin x$ and $\cos x$), a common technique is to transform the integrand into a form involving $\tan x$ and $\sec^2 x$ (or $\cot x$ and $\csc^2 x$). This allows for a straightforward $u$-substitution. The power rule for integration, $\int x^n dx = \frac{x^{n+1}}{n+1} + C