Solving for Alpha in Mechanics: Trig Formulas and Force Components

[CivilSigma]

So I have a mechanics question 2.65 of which I have deduced the following :
$$x-Component of all forces$$
$$F1 = 150 cos30$$
$$F2= 150 cos \alpha$$
$$F3 = 150 cos(\alpha+50)$$

$$y-Components of all forces$$
$$F1 = -150 sin30$$
$$F2 = 150 sin \alpha$$
$$F3 = 150 cos(50-\alpha)$$

Finally, $$R = \sqrt{(\Sigma Fx)^2 + (\Sigma Fy)^2}$$

Now we know the resultant is at max 600 N, how do we go about solving $$\alpha$$ ? I tried applying various trig formulas like angle addition and subtraction, but I couldn't isolate $$\alpha$$. How would you go about solving for alpha?

 

[mfb]

Set R to 600N, then plug everything in and see what you get (and please write it down here, so we can see where exactly you get stuck).