Three friends - Javish, Ravi and Renu are playing hide and seek in a park. Javish and Ravi were supposed to hide and Renu had to find both of them. If the positions of three friends are at \(A\), \(B\) and \(C\) respectively as shown in the figure and forms a right-angled triangle such that \(AB = 9 \ m\), \(BC = 3 \sqrt{3} \ m\) and \(B = 90^\circ\).
Based on the above information, solve the following questions:
1. Find the measure of \(\angle A\) using trigonometric ratio.
2. Find the length of \(AC\).
3. \(\cos^2 \theta = \)
4. \(1 + \cot^2 \theta =\)