5. The point \(P\) lies on the curve with equation
$$x = ( 4 y - \sin 2 y ) ^ { 2 }$$
Given that \(P\) has \(( x , y )\) coordinates \(\left( p , \frac { \pi } { 2 } \right)\), where \(p\) is a constant,
- find the exact value of \(p\).
The tangent to the curve at \(P\) cuts the \(y\)-axis at the point \(A\).
- Use calculus to find the coordinates of \(A\).