Answer
The bicyclist has to apply a force of $405.8N$ to climb the hill.
Work Step by Step
1) The bicyclist goes downhill
As shown in image a) below, the force $m\vec{g}\sin\theta$ causes the bicyclist to be able to go downhill. However, this motion is opposed by air resistance force $\vec{R}$. Since the bicyclist is in constant velocity, these 2 forces cancel each other out.
$$R=mg\sin\theta=80\times9.8\times\sin15=202.9N$$
2) The bicyclist goes uphill
To be able to go uphill, the bicyclist has to apply a force $\vec{F}$ directed uphill. This force is opposed by both the weight of the bicyclist $m\vec{g}\sin\theta$ and air resistance $\vec{R}$. As the bicyclist remains at the same constant speed, again we have $$F=mg\sin\theta+R=2\times202.9=405.8N$$
