what does 45 degree phase excitation angle correspond to in scan angle?

I changed the progressive phase excitation angle (beta) to 45 degrees on my dipole array, and I got huge gain (better than the endfire 32-degree phase at 0-degree scan angle). I am not sure what the 45-degree phase excitation angle corresponds to in scan angle (theta) as when I plug it in the equation beta = -kd cos(theta), beta=45 and d=0.1lambda, then I get errors for theta? I wonder what the theta for 45-degree phase is? The radiation pattern for 45-degree phase is the same as the 32-degree phase for endfire.

Thanks.