Is it possible to align roots to plot consistently?

Question

I made a routine to find roots of the equation for a specific range of input angle. For this model, usually total number of roots is 10, however at some angles total number of roots is 8. Because of this, a table with a list of roots has some rows misaligned roots. When plotting, I end up with zig-zagging line instead some curve. For this case, see row 11th for example. It has 8 roots. By looking at the numbers (see first column of the same row) , I can see 8th root should be 10th, 7th root should be 9th and 6th root should be 8th. And the empty columns for 11th row should be 6 and 7. Is it possible to do root finding thouroughly and alligned properly so that plot can be made consistently?

f[a_]:=Sin[a]*Cos[a]+Sin[a]*x^2-Cos[a]*x^4+(Sin[a]-Cos[a])*x^6-(Sin[2*a]-Cos[2*a])*x^8+(Sin[1*a]-Cos[1*a])*x^10;
roots = Table[x /. NSolve[f[angle] == 0], {angle, 0, 2*Pi, Pi/40}];
roots // TableForm

WolfMath V9

Answer 1

Writing:

f[a_] := Sin[a] Cos[a] + Sin[a] x^2 - Cos[a] x^4 + (Sin[a] - Cos[a]) x^6 -
         (Sin[2 a] - Cos[2 a]) x^8 + (Sin[a] - Cos[a]) x^10;

roots = Table[If[Sin[angle] - Cos[angle] != 0, x /. NSolve[f[angle] == 0], 
                 ## &[]], {angle, 0, 2 Pi, Pi/40}];

roots // TableForm

you get a table without the two rows where, by canceling the coefficient of the tenth grade degree, the solutions are 8 rather than 10.