In a uniform linear array four isotropic radiating elements

In a uniform linear array four isotropic radiating elements are spaced λ/4 apart. The progressive phase shift between the elements required for forming the main beam at 60º off the end fire is—

For λ/4 separated isotropic source, phase is given by
ψ = β d cos φ + α
for end fire array α = – βd
so we get
ψ = βd (cos φ – 1)
where,
φ = 60º

d =	λ	, β =	2π
	4		λ

d =	2π	,	λ	= (0.5 - 1)
	4		4

=	π
	4