Question 1009944
If sin(theta)/2 = 1/m, we can plug in for m and get
sin(theta)/2 = 1/(5/4) = 4/5 = .8
Now take the inverse sin of both sides and get
(theta)/2 = sin^(-1) .8 = 53.1 and 
theta = 106.2 degrees
Not really a half-angle formula question, that is, it does not involve that identity...