Maybe it's me, but this didn't seem easy!?!? I'm getting an answer of sin a = 1; is this correct?

Here's a summary of what I did:

You have the cosine of a difference identity:

(Eq1)

Use the Law of sines to write sin b in terms of sin a:

(Eq2)

Use the pythagorean identity to write cosine in terms of sine:

(Eq3a)

(Eq3b)

Plug (2), (3a), and (3b) into (1), plus the fact that cos (a-b) = 3/4:

(Eq4)

Solved for sin a and I got sin a = 1.

I'm sure I did something wrong here.