Any suggestion on how to integrate this trig equation?

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corona7w
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I am absolutely stoned by this equation. I've looked through all the trig identities and the only one that comes close to be used in here is sin2u = 2sin(u)cos(u), but there is that lamba... Any suggestions?
 

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The λ in that integral is just another constant, no different than 2.

Hint: What is sin(a+b) + sin(a-b)?