Let the function $$f(\theta) = \begin{vmatrix} \sin \theta & \cos \theta & an \theta \\ \sin(\pi/6) & \cos(\pi/6) & an(\pi/6) \\ \sin(\pi/3) & \cos(\pi/3) & an(\pi/3) \end{vmatrix}$$ where $\theta \in \left[\frac{\pi}{6}, \frac{\pi}{3}\right]$ and $f^{\prime}(\theta)$ denote the derivative of $f$ with respect to $\theta$. Which of the following statements is/are TRUE? (I) There exists $\theta \in \left(\frac{\pi}{6}, \frac{\pi}{3}\right)$ such that $f^{\prime}(\theta) = 0$. (II) There exists $\theta \in \left(\frac{\pi}{6}, \frac{\pi}{3}\right)$ such that $f^{\prime}(\theta) \neq 0$.

Let the function f( ) = vmatrix & & an \\ ( /6) & ( /6) & an( /6) \\ ( /3) & ( /3) & an( /3) vmatrix where [ 6, 3 ] and f'( ) denote the derivative of f with respect to . Which of the following statements is/are TRUE? (I) There exists ( 6, 3 ) such that f'( ) = 0. (II) There exists ( 6, 3 ) such that f'( ) 0.

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