My current plans, and a small (or not) puzzle

High school is coming up, life is getting jam-packed.  My focus is getting better though so it may get easier later.

See the "The Puzzle" section below for the actual puzzle!

I'm in marching band and have marching camp this week and on top of that I do a 2-hour math class and practice sax like crazy and maybe I do a bit of reverse engineering / software development just to relax, and I'm already out of time—sleeping only 8 hours a night.  I don't know how manageable real high school work is by this point.  So probably not posting here a lot.

So a puzzle for y'all to grind while you wait for new posts.  Note -- I posted this publicly to see if other solutions are significantly more complex, but that required me to write up my own approach.  So don't search online unless you want spoilers.

The puzzle

Find $\tan\theta$ if

$$\sin^2\theta + x^2 + x\sqrt3 \sin\theta = 3,$$

$$\cos^2\theta + x^2 + x \cos \theta = 4{,}$$

where $0<\theta<\frac\pi2$ and $x>0$.

EDIT: The solution is out!