Question: how to get different definitional domain!

Dear all:

   suppossed i have a function as following :


where  x is belong to (0,Pi/2), I3,I5 is defined to I3^2+I5^2 < .232.

i have ploted some curves of f(x) . As to different I3 and I5, the curve of f(x) have different point of intersection with y=1 function, may one point or two  point or three where 0<x<Pi/2.

So i want to know which range of I3,I5 , f(x) have one point with y=1, which range of I3,I5, f(x) have two point with y=1,....... 

Notes : if no methods to get exaclty value of I3,I5, the curves is also OK?

tks very much ,looking forward to your reply!

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