(*reciprocal BCC lattice- XRD angles*)
angbccr[k_] := ((ArcSin[Sqrt[#1]/((2*k)/Pi)]*2*180)/Pi & )[listbcc]

lk[n_, m_, l_] := kk[n, m, l] . kk[n, m, l]

kk[n_, m_, l_] := n*b1[[1]] + m*b2[[1]] + l*b3[[1]]

a = Pi

bccr := {b1 = (Pi*{ez + ey - ex})/a; b2 = ({ex + ez - ey}*Pi)/a;
     b3 = (Pi*{ex + ey - ez})/a; }

xyz:={ex={1, 0, 0}; ey={0, 1, 0};
         ez={0, 0, 1};}

list1=Range[20]

Out[68]= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

Table[lk[n,m,l], {n,-2,2}, {m,-2,2}, {l,-2,2}];

Flatten[%]

Out[70]= {12, 11, 16, 27, 44, 11, 8, 11, 20, 35, 16, 11, 12, 19, 32, 27, 20,

>    19, 24, 35, 44, 35, 32, 35, 44, 11, 8, 11, 20, 35, 8, 3, 4, 11, 24, 11,

>    4, 3, 8, 19, 20, 11, 8, 11, 20, 35, 24, 19, 20, 27, 16, 11, 12, 19, 32,

>    11, 4, 3, 8, 19, 12, 3, 0, 3, 12, 19, 8, 3, 4, 11, 32, 19, 12, 11, 16,

>    27, 20, 19, 24, 35, 20, 11, 8, 11, 20, 19, 8, 3, 4, 11, 24, 11, 4, 3, 8,

>    35, 20, 11, 8, 11, 44, 35, 32, 35, 44, 35, 24, 19, 20, 27, 32, 19, 12,
      
>    11, 16, 35, 20, 11, 8, 11, 44, 27, 16, 11, 12}


listbcc=Intersection[%%%, list1]

Out[73]= {3, 4, 8, 11, 12, 16, 19, 20}


Example:
In[75]:= angbccr[20.]
Out[75]= {15.6369, 18.0749, 25.67, 30.1979, 31.575, 36.6201, 40.0399, 41.1264}