In this paper we continue our program, started in [2], of building up
explicit generalized Euler angle parameterizations for all exceptional compact
Lie groups. Here we solve the problem for E7, by first providing explicit
matrix realizations of the Tits construction of a Magic Square product between
the exceptional octonionic algebra J and the quaternionic algebra H, both in
the adjoint and the 56 dimensional representations. Then, we provide the Euler
parametrization of E7 starting from its maximal subgroup U=(E6 x U(1))/Z3.
Next, we give the constructions for all the other maximal compact subgroups.Comment: 23 pages, added sections with new construction
