Three friends - Vinay, Lithik and Rithu are playing hide and seek in a park. Vinay and Lithik were supposed to hide, and Rithu 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 \(AB = 9 \ m\), \(BC = 9 \ m\) 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. \(1 + \cot^2 \theta =\)