nl(lambda) = 2d sin q(theta)---- eq(1)

1/d2 = 4/3[(h2+hk+k2)/a2]+1/c2------ eq(2)

By applying these two equations, you can calculate the exact value of theta for heagonal crystal structure.

There are a lot of free programs available. One is PowderCell which enables the input of lattice parameters, space groups number and after closing the editor the POSITIONS of peaks can be calculated. For the correct intensities you need to know the structure. I guess you are asking for hcp metals. The trick is that for these metals the atom position is not 0,0,0 as many people assume, but 1/3, 2/3, 1/3. Then you only need to enter the lattice parameters for each of the metals and define the periodic number. 

 If you cannot calculate theta value, I think the problem is to calculate plane spacing d.   Please try the formula 1/d2 = 4(h2 + hk+ k2)/3/a2 + l2/c2, see attachment for derivation.

you may check your theta result with PowderCell, http://www.ccp14.ac.uk/ccp/web-mirrors/powdcell/a_v/v_1/powder/e_cell.html 

If you have h, k, l, a and c, then for hexagonal system use:

1/d2 = (4/3){(h2 + hk + k2)/a2} + (l2/c2)

and theta = (arcsin(Lambda/2d)) for each value of hkl

Use Hull-Davey chart. See attached chart I have constructed for the use of my students

In my work for Cd, Co and Zn based hcp-ccp binary solid solution, the same can be correlated by simulating the 2 theta based on hkil as well as d-spacing,using self designed crystal hack program.

Link: http://crystalhack.blogspot.com/

http://crystalhack.blogspot.com/