Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.5 L'Hopital's Rule; Indeterminate Forms - Exercises Set 6.5 - Page 448: 9

$1$

Since the limit as theta approaches zero is $\frac{0}{0}$, L'Hopital's Rule can be used. The derivative of the numerator and denominator is performed, leaving $$\lim\limits_{\theta \to 0}sec^{2} \theta=sec^{2}(0)=1^{2}=\boxed{1}.$$