他试图去讨好她, I get the meaning but what is the nuance of removing 去 to connect the two actions?
This would be my answer
来(to) emphasize the mean
去(to) emphasize the objective
他试图用花去讨好她 - "去" emphasizes the objective is to 讨好她
他试图用花來讨好她 - "來" emphasizes the mean is 花
An infinitive phrase is formed when 去 is placed after a verb to indicate the inclination to do something:
他试图去讨好她 - He "tries to" cozy up to her.
他希望去國外唸書 - He "wishes to" go abroad to study.
難民都逃去山中了 - Refugees have already "escaped to" the mountains.
Note: For cases 2 & 3, "去" can't be eliminated for it contains the direction message "from here go there", and, "來" can be used in place of "去" with directions changed to "from there come here".
When 來 is placed after a verb, it forms a verbal phrase or "estimate that":
看來不是他 - It "looks like" not him/"Estimate that" it is not him.
說來你不會相信 - "Estimate that" you won't believe.
想來你同意了 - "Estimate that" you have agreed.