Consider the following for the next two (02) items that follow :

Let $x=\frac{\sin ^2 A+\sin A+1}{\sin A}$ where 0 < A ≤ $\frac{\pi}{2}$

At what value of A does x attain the minimum value ?

Consider the following for the next two (02) items that follow :

Given that

sinx + cosx + tanx + cotx + secx + cosecx = 7 

The given equation can be reduced to 

Consider the following for the next two (02) items that follow :

Given that

sinx + cosx + tanx + cotx + secx + cosecx = 7 

If sin2x = a - b√c, where a and b are natural numbers and c is prime number, then what is the value of a - b + 2c ? 

Consider the following for the next two (02) items that follow :

Given that m(θ) = cot²θ + n²tan²θ + 2n, where n is a fixed positive real number. 

What is the least value of m(θ) ?