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Simplification question in Mathematica 7

• To: mathgroup at smc.vnet.net
• Subject: [mg113840] Simplification question in Mathematica 7
• From: Jennifer Hatz <btjunkie.org at abv.bg>
• Date: Mon, 15 Nov 2010 05:50:38 -0500 (EST)

 Both FullSimplify and Simplify do nothing on the following expression
Sqrt[-(((ea - eb)^2 + (na - nb)^2)*(-mb1^2 - mb2^2 + mb2^2*Cos[2*b1] + mb1^2*Cos[2*b2])*Csc[b1 + b2]^4)]/Sqrt[2]

I found out that it is possible to further simplify it to
Sqrt[((ea - eb)^2 + (na - nb)^2)*Csc[b1 + b2]^4*(mb2^2*Sin[b1]^2 + mb1^2*Sin[b2]^2)]

as
FullSimplify[Sqrt[(-(ea - eb)^2 - (na - nb)^2)*(-mb1^2 - mb2^2 + mb2^2*Cos[2*b1] + mb1^2*Cos[2*b2])*Csc[b1 + b2]^4]/Sqrt[2] - Sqrt[((ea - eb)^2 + (na - nb)^2)*Csc[b1 + b2]^4*(mb2^2*Sin[b1]^2 + mb1^2*Sin[b2]^2)]]
produces zero

The question is - is it somehow possible to tell mathematica to convert the first expression into the second?
Are there any additional commands that work on trigonometric functions better than Simplify?

Thanks in advance