Since that involves G both as the argument of a transcendental function (sine) and outside of it, there will not be any simple algebraic solution. You will have to use a numerical solution.
Where G is the angle to the edges of the water and is less then Pi radians, from the centre of the pipe. R is a known from the Manning Formula as we solve for it from V and a known Slope. r is the radius of the pipe in Feet and is chosen based on the community size. How do we solve for the Angle G?
I am looking for a numerical value. We have other formulae that supply the person with a value for R and r. We currently have them guessing at values for G until the get one where the (Sin G)/G is approx equal to the Left Side (LS) of the equation.