The value of [tex]\tan 1^{\circ}\tan 2^{\circ}+\tan 2^{\circ}\tan 3^{\circ}+\tan 3^{\circ}\tan 4^{\circ}+\cdots+\tan 88^{\circ}\tan 89^{\circ}[/tex] can be expressed in the form [tex]\cot^2 1^{\circ}-n[/tex]. What is the value of [tex]n[/tex]?