To find the power of the engine, we first need to determine the driving force (DF) using the equation for power:

\(DF = \frac{P}{v}\)

where \(P\) is the power and \(v = 15 \text{ m/s}\) is the speed of the train.

Using Newton's second law, the equation for the forces acting on the train is:

\(DF - 240,000g \sin 4^{\circ} - 18,000 = 240,000 \times (-0.2)\)

Solving for \(DF\):

\(DF = 240,000 \times 9.8 \times \sin 4^{\circ} + 18,000 - 240,000 \times 0.2\)

Substitute \(DF\) back into the power equation:

\(P = DF \times 15\)

Calculate \(P\) to find:

\(P = 2,060,000 \text{ W}\)