Solving for unknown variable

Its always a good idea to attach the Prime sheet itself and also state which version you are using (especially if you don't use the latest current version).

In the meantime you provided your sheet and also told us that you are using P10.

Actually what you did in your sheet worked, even though the result seems to look somewhat strange. The reason for this is that the symbolic engine in Prime unfortunately does not know anything about units and treats units as unknown variables. So it can't simplify the result.

A numeric evaluation (a simple = at the end) can do the job:

For this numeric evaluation to work you have to activate "Units/Constants in Symbolics" in the Calculation Options and then recalc the worksheet (Ctrl+F5). The symbolics still does not know anything about units but this option should ensure that units and constants (like g) remain labeled as units or constants.

As we can see returns the symbolics two different solutions and both are correct. Actually your equation has an infinite number of solutions.
The "assume" modifier should be able to select the solutions within a desired range, but this usually does not work as expected and in your case we have the additional problem of the units which the symbolics can't handle.

As you are just after a numeric result, I would second Terry's suggestion to use a numeric method like the "root" function. To be able to do so you have to get rid of the red errors (which affect the numeric engine but not the symbolic) by turning the expressions into function of the unknown angle theta as shown by Terry.

Then based on the equation you want to solve define a function f(theta) with the solutions as its zeros.

This function can now be used in the "root" function to get the solution within a desired range. You may be interested in the solution which is greater than zero but smaller than 360°

The "root" can also be used in a second way by providing a guess value:

As the last example shows there is no guarantee that the solution found will be near the guess, though.

Prime 10 sheet attached