Find and simplify the first three terms in the expansion, in ascending powers of \(x\), of \(\left( 2 + \frac { 1 } { 3 } k x \right) ^ { 6 }\), where \(k\) is a constant.
In the expansion of \(( 3 - 4 x ) \left( 2 + \frac { 1 } { 3 } k x \right) ^ { 6 }\), the constant term is equal to the coefficient of \(x ^ { 2 }\).
Determine the exact value of \(k\), given that \(k\) is positive.