Question: Solving multiple phase angles for multiple equations

Greetings All

I have several equations and each have their own individual frequencies and amplitudes. I would like to sum the equations together and adjust ONLY the individual phases, phase1,phase2, and phase3 to keep the total amplitude value of eq_total under a specific value like 0.8. I know I can normalize the signal or change the vertical offset, but for my purposes I need to have the amplitude controlled by changing/finding the values for just the phases in phase1,phase2, and phase3 that will do this.

Example:
eq1=0.2*cos(2pi*t*3+phase1)+vertical offset1
eq2=0.7*cos(2pi*t*9+phase2)+vertical offset2
eq3=0.8*cos(2pi*t*5+phase3)+vertical offset3

eq_total=eq1+eq2+eq3

Is there a way to solve for phase1,phase2, and phase3 so that the amplitude of the summed signals in eq_total never goes over 0.8 by just adjusting/finding the values of phase1,phase2,and phase3?

Do I have to use for loops to run through each phase and do a test?

Here's a picture of a geogebra applet I tested this idea with.

http://dl.dropbox.com/u/6576402/questions/ggb/amp_phase_pic.png

Here's a link to the file if you want to interact with it in geogebra (the latest geogebra is needed)

http://dl.dropbox.com/u/6576402/questions/ggb/sin_find_phases_example.ggb