Classical Mechanics - Special Interest Problem

In problem 1-15, you showed that an orthogonal "3-D" rotation of the form

must have a = 1 /2 corresponding to a -45^o rotation about the x₁ axis. It is easy to visualize that the only rotation angle that creates the same magnitude angle between all the other axes must be +/-45^o. Now consider a rotation about the x₁ axis in 4-D space that has the following form.

1. For what angle of rotation about the x₁ axis is this valid?
2. Are there any other valid rotations with this form, in which the magnitude  of the elements in the subgroup l₂₂ to l₄₄ are the same? (Hint: Consider the role of the "-" sign(s).)

Hardcopy entries should be submitted in class by noon on Monday of next week. Answers should be concise but complete.