The value of \[ \frac{15^3 + 6^3 + 3 \cdot 6 \cdot 15 \cdot 21}{1 + 4(6) + 6(36) + 4(216) + 1296} \] is equal to:
If \[ f(x) = \frac{1}{x^2 + 4x + 4} - \frac{4}{x^4 + 4x^3 + 4x^2} + \frac{4}{x^3 + 2x^2}, \] then the value of \[ f\left(\frac{1}{2}\right) \] is equal to: