We want the regions 1, 2, and 3 to each be 1/3 Pi (2 R)^2. and since there are two variables, R1 and R2, we shall get two conditions in the two unknowns.

Input := 


Area1[R1_] = Integrate[(2 R1 Sin[t])^2,{t,0, Pi}]

Output =


       2

2 Pi R1

Input := 


Area2[R1_,R2_] = Integrate[(2 R2 Sin[t])^2,{t,0, Pi}] -

						Area1[R1]

Output =


        2          2

-2 Pi R1  + 2 Pi R2

Input := 


Area3[R2_] = Pi (2 R) ^2 - Area1[R1] - Area2[R1,R2]

Output =


      2          2

4 Pi R  - 2 Pi R2