First step is to solve equations (i) and (ii) for and . Multiply (i) by , multiply (ii) by , and subtract. That gives (using the trig formula ). Therefore . A similar procedure (multiplying (i) by and (ii) by ) gives .

Now square both of those expressions, and substitute those formulas for and into (iii). You'll find that after a bit of simplification and cancellation, it reduces to . Note: , not as (wrongly) stated in the question. Note also the missing in equation (ii).