The latitude at which heat gain through insolation approximately equals heat loss through terrestrial radiation is at \(66^{\circ}\) North and South.
At these latitudes, near the poles, there is a balance between the heat received from the Sun (insolation) during the day and the heat radiated away from the Earth's surface during the night, resulting in a relatively stable temperature regime. This is one of the factors contributing to the formation of the polar climates.
So, the correct option is \((D): 66^{\circ}\) North and South