Let's suppose that we are climbing at 100 kts airspeed, producing our best angle of climb in still air.
If we meet a 90 knot headwind and reduce our airspeed to 90 knots will be in a vertical climb. So going slower in a headwind increased our climb angle.
If the headwind then increases to 110 knots we will need to increase our airspeed to 110 knots to restore our vertical climb. So going faster in a headwind increased our climb angle.
Curiouser and curiouser!!
So depending on the relationship between our airspeed and our headwind, we may need to increase or decrease our airspeed to maximise our climb angle.