Translation:He was learning to do it with a new tool.
"He was learning how to do it with a new tool." Wouldn't this sentence be acceptable? The meaning is the same.
The semantics are pretty much the same, but if you insert "how", the correct czech would be "učil se jak to dělat novým nástrojem", notice the insertion of "jak"="how"
I just fell into this trap THREE times in my last practice session. Talk about force of habit...
"He was learning to do it with the new tool" seems like it should be accepted. Up to this point, "a" and "the" have generally been interchangeable, and in this context retains much the same meaning.
They are not interchangeable and they were not. They are used in different situations in English which may or may not correspond to different sentences in Czech.
In certain sentences using "the" if there is no demonstrative pronoun in Czech is aaccepted if such a sentence makes good sence when it would be understood from context which particular iem it was. I do not see that likely to be said this way here.