Summing sines of different frequencies Is there a general formula for solving the following equation:
$$A \sin(Bt+C) + D \sin(Et+F) = G \sin(Ht+I)$$
All constants on the left side of the equation are known (t is a variable). Is there a formula for calculating G, H and I? Is this even solvable in general? 
I searched the web and found some semi-relevant hits, like here, but it didn't really seem to answer my question. 

I'm not sure about a general formula, but to your answer wether it is solvable in general: the function $sin(3x+4)+sin(6x+7)$ is clearly not harmonic (you can see this by simply plotting it), providing a counterexample to the statement.
