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\Delta T  \left(-\tan \left(\psi _E\right) \sin \left(\psi _N\right) \left(\delta \omega _D-\omega _{\text{ie}} \cos (L) \left(\cos \left(\psi _D\right) \sin \left(\psi _E\right) \cos \left(\psi _N\right)+\sin \left(\psi _D\right) \sin \left(\psi _N\right)\right)+\omega _{\text{ie}} \sin (L) \cos \left(\psi _E\right) \cos \left(\psi _N\right)-\omega _{\text{ie}} \sin (L)\right)+\tan \left(\psi _E\right) \cos \left(\psi _N\right) \left(\delta \omega _E-\omega _{\text{ie}} \cos (L) \left(\cos \left(\psi _D\right) \sin \left(\psi _E\right) \sin \left(\psi _N\right)-\sin \left(\psi _D\right) \cos \left(\psi _N\right)\right)+\omega _{\text{ie}} \sin (L) \cos \left(\psi _E\right) \sin \left(\psi _N\right)\right)+\tan \left(\psi _E\right) \sin \left(\psi _N\right) \left(\omega _{\text{ie}} \sin (L) \cos \left(\psi _E\right) \cos \left(\psi _N\right)-\omega _{\text{ie}} \cos (L) \left(\cos \left(\psi _D\right) \sin \left(\psi _E\right) \cos \left(\psi _N\right)+\sin \left(\psi _D\right) \sin \left(\psi _N\right)\right)\right)+\tan \left(\psi _E\right) \cos \left(\psi _N\right) \left(\omega _{\text{ie}} \sin (L) \left(-\cos \left(\psi _E\right)\right) \sin \left(\psi _N\right)-\omega _{\text{ie}} \cos (L) \left(\sin \left(\psi _D\right) \cos \left(\psi _N\right)-\cos \left(\psi _D\right) \sin \left(\psi _E\right) \sin \left(\psi _N\right)\right)\right)\right)+1
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\begin{eqnarray}
&&\Delta T  \bigg(-\tan (\psi_E) \sin (\psi _N) \bigg(\delta \omega _D-\omega _{ie} \cos (L) \bigg(\cos (\psi _D) \sin (\psi _E) \cos (\psi _N)+\sin (\psi _D) \sin (\psi _N)\bigg)\notag\\
&&+\omega _{ie} \sin (L) \cos (\psi_E) \cos (\psi _N)-\omega _{ie} \sin (L)\bigg)\notag\\
&&+\tan (\psi _E) \cos (\psi _N) \bigg(\delta \omega _E-\omega _{ie} \cos (L) (\cos (\psi _D) \sin (\psi _E) \sin (\psi _N)-\sin (\psi _D) \cos (\psi _N))\notag\\
&&+\omega _{ie} \sin (L) \cos (\psi _E) \sin (\psi _N)\bigg)+\tan (\psi _E) \sin (\psi _N) (\omega _{ie} \sin (L) \cos (\psi _E) \cos (\psi _N)\notag\\
&&-\omega _{ie} \cos (L) (\cos (\psi _D) \sin (\psi _E) \cos (\psi _N)+\sin (\psi _D) \sin (\psi _N)))\notag\\
&&+\tan (\psi _E) \cos (\psi _N) \bigg(\omega _{ie} \sin (L) (-\cos (\psi _E)) \sin (\psi _N)-\omega _{ie} \cos (L) (\sin (\psi _D) \cos (\psi _N)\notag\\
&&-\cos (\psi _D) \sin (\psi _E) \sin (\psi _N))\bigg)\bigg)+1
\end{eqnarray}
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