It depends on the game system and the game master, as well as the other players.
In many role-playing games, the tactics of the fictional situation being represented are not modeled directly, and so a character's tactical competence can be entirely abstracted into their character description, and the player doesn't need to understand much about tactics, because they don't exist in the game mechanics.
In some other role-playing games, there are tactical factors of the fictional situation which are represented with some accuracy in the game mechanics, and so for those games, it can be very useful to learn the actual tactics of those situations and apply them in the game.
In all games, there are some mechanics of the game itself which can be played to advantage, which don't relate to the fictional situation but still affect how effective your character is.
So, when playing a character who is an experienced combatant, as a player who is not very familiar with the tactics of the fictional situation and/or game system, I'd say it makes sense to expect the game master (and/or the most tactically experienced player(s) in the group) to support your character's competence. Depending on their agreement with this, and the style of play, you could:
- Explain and discuss this situation before play begins, so other players aren't surprised and can agree to help you out as needed. (Or, so they can refuse in advance, to avoid problems during play.)
- Ask others for information and understandings of situations that your character should have but that you don't.
- During play, before just stating that your character takes tactical actions or gives orders, either start with a proviso (such as: "Assuming my character doesn't know better..." or "Unless this is tactically foolish..."), or if you know you don't know what makes sense, ask for help (e.g. "Ok I know we've got to deploy carefully here, but don't know what makes sense, so what might my character suggest here?").
Eventually, this can become more expected and natural. At least with groups I've played in or run, the new players get used to asking or being corrected, the experienced players or GM get used to helping and checking bad moves, it can flow naturally and gets more natural, and before long, the new players need less and less help and can do it themselves.
However, if the experience level of some players is higher than others, and if some players are more competitive (or apathetic or mean) than cooperative, and the game master doesn't intervene, there can be some issues. (You didn't ask about that and there are many possible problems, so I won't get into examples.)
In your specific example, it sounds like there are many fields where this sort of thing is going to come up, since characters are invited to have all these PhD's and so on which presumably none of the players have. Therefore I would expect that it is entirely reasonable for players to say they want to apply their characters' knowledge, and collaborate a bit with the GM and/or other players to produce the specifics, since clearly players don't magically become knowledgeable of anything on their characters' sheets.
Also, your character has some fairly unique abilities (sniper with invisibility and illusions) which by its nature I would say is actually going to be most effective the more creative you are and the less predictable you are, so even though you could find some fictional examples in film, sci fi, comics, etc., I think you'll do best using your imagination as long as what you come up with makes sense. Actually, what I would do would be to look to examples of invisible illusionists in fiction as inspiration, but only do what they do against typical foes. When you have a harder situation, think of what people have done before, and do something that seems to be doing that, but actually be doing something else that is using that idea as bait.
For example, in Predator (1987), the heroes have a horrible time fighting a ranged attacker who is almost invisible. The attacker shoots from jungle cover and then gives a hint of movement, getting everyone to fire but miss. That's not bad but typical. Your character could shoot someone from a direction no one is looking, so no one knows where you are, then create an illusion of nearly-invisible movement in a direction you aren't (but perhaps where something you happen to want destroyed is), wait for them to notice that illusion and blast away at that, while you slip away or do something else.
