Trigonometric equation with power 2

I would like to silmplify a trigonometric equation with some power 2. I'm sure this equation can be reduced but i didn't manage tyo simplify it with Mathematica.

May you help me to simplify this trigonometric equation?

Expr=(1/(cr^4))(4 cr^2 (zP3 - zP4 + pr (Cos[γ3] - Cos[γ4]) +
mr (Cos[γ3 - ϕ3] - Cos[γ4 - ϕ4]))^2 +
4 cr^2 (-xP3 + xP4 + pr (-Sin[γ3] + Sin[γ4]) +
mr (-Sin[γ3 - ϕ3] +
Sin[γ4 - ϕ4]))^2 - ((xP3 - xP4)^2 + (zP3 -
zP4)^2 - 2 pr^2 (-1 + Cos[γ3 - γ4]) -
2 mr^2 (-1 + Cos[γ3 - γ4 - ϕ3 + ϕ4]) +
2 pr ((zP3 - zP4) (Cos[γ3] - Cos[γ4]) + (xP3 -
xP4) (Sin[γ3] - Sin[γ4])) -
2 mr (-(zP3 - zP4) (Cos[γ3 - ϕ3] -
Cos[γ4 - ϕ4]) +
pr (Cos[γ3 - γ4 - ϕ3] - Cos[ϕ3] -
Cos[ϕ4] +
Cos[γ3 - γ4 + ϕ4]) + (xP3 -
xP4) (-Sin[γ3 - ϕ3] +
Sin[γ4 - ϕ4])))^2)

I would like simplification if time the pattern cos()^2+sin()^2 appears.

• Are you after Simplify@TrigExpand@Expr? – corey979 Sep 20 '16 at 15:19
• Do you have some ideas to reduce this expression ? The FullSimplify function doesn't permit to reduce the power 2. Thank you for your help – Bendesarts Sep 21 '16 at 8:28