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

In a triangle POR, P is the largest angle and cosP = $\frac{1}{3}$. Further the in-circle of the triangle touches the sides PQ, QR and RP at N, L and M respectively such that the lengths PN, QL and RM are n, n + 2, n + 4 respectively where n is an integer. 

What is the length of the smallest side ?

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 :

A quadratic equation is given by

(3 + 2√2)x² - (4 + 2√3)x + (8 + 4√3) = 0

What is the HM of the roots of the equation ?