Edit detail for #411 "forbidden" type generated by trigonometric expression revision 1 of 5

changed:
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The following challenge posted by Vladimir yields 'EXPR COMPLEX FRAC INT' as result type.  I think it should be 'EXPR COMPLEX INT'.  Declaring the variable helps.

\begin{axiom}
ex1 := cot(1/2*(3/8*%pi*2^(1/2)-1/2*2^(1/2)*atan(3/5)-1/4*2^(1/2)*atan(27+73/4*2^(1/2))-1/4*2^(1/2)*atan(42/41+12/41*2^(1/2))+1/4*2^(1/2)*atan(144/103+148/103*2^(1/2))-1/4*%i*2^(1/2)*atanh(-51945/813577+28/2440731*((714295812*(833932+86508*93^(1/2))^(1/3)-4881462*(833932+86508*93^(1/2))^(2/3)+3963747144)/(833932+86508*93^(1/2))^(1/3))^(1/2)+28/2440731*6^(1/2)*((238098604*(833932+86508*93^(1/2))^(1/3)*((714295812*(833932+86508*93^(1/2))^(1/3)-4881462*(833932+86508*93^(1/2))^(2/3)+3963747144)/(833932+86508*93^(1/2))^(1/3))^(1/2)+813577*((714295812*(833932+86508*93^(1/2))^(1/3)-4881462*(833932+86508*93^(1/2))^(2/3)+3963747144)/(833932+86508*93^(1/2))^(1/3))^(1/2)*(833932+86508*93^(1/2))^(2/3)-660624524*((714295812*(833932+86508*93^(1/2))^(1/3)-4881462*(833932+86508*93^(1/2))^(2/3)+3963747144)/(833932+86508*93^(1/2))^(1/3))^(1/2)+4852325397096*(833932+86508*93^(1/2))^(1/3))/(833932+86508*93^(1/2))^(1/3)/((714295812*(833932+86508*93^(1/2))^(1/3)-4881462*(833932+86508*93^(1/2))^(2/3)+3963747144)/(833932+86508*93^(1/2))^(1/3))^(1/2))^(1/2))+1/8*%i*2^(1/2)*log(18/7)+1/8*log(81*(69/97+2/97*2^(1/2))^(%i*2^(1/2))*((26+7*%i-(10+4*%i)*2^(1/2))*(1/3+1/18*6^(1/2)*((62*(1052+108*93^(1/2))^(1/3)+(1052+108*93^(1/2))^(2/3)+28)/(1052+108*93^(1/2))^(1/3))^(1/2)+1/18*((744*(1052+108*93^(1/2))^(1/3)*((62*(1052+108*93^(1/2))^(1/3)+(1052+108*93^(1/2))^(2/3)+28)/(1052+108*93^(1/2))^(1/3))^(1/2)-6*((62*(1052+108*93^(1/2))^(1/3)+(1052+108*93^(1/2))^(2/3)+28)/(1052+108*93^(1/2))^(1/3))^(1/2)*(1052+108*93^(1/2))^(2/3)-168*((62*(1052+108*93^(1/2))^(1/3)+(1052+108*93^(1/2))^(2/3)+28)/(1052+108*93^(1/2))^(1/3))^(1/2)+2376*6^(1/2)*(1052+108*93^(1/2))^(1/3))/(1052+108*93^(1/2))^(1/3)/((62*(1052+108*93^(1/2))^(1/3)+(1052+108*93^(1/2))^(2/3)+28)/(1052+108*93^(1/2))^(1/3))^(1/2))^(1/2))/(3+2^(1/2)))^(2*%i*2^(1/2))/((2+3*%i-2*%i*2^(1/2))^(4*%i*2^(1/2))))-acoth(2))*2^(1/2));
\end{axiom}

axiom
ex1 := cot(1/2*(3/8*%pi*2^(1/2)-1/2*2^(1/2)*atan(3/5)-1/4*2^(1/2)*atan(27+73/4*2^(1/2))-1/4*2^(1/2)*atan(42/41+12/41*2^(1/2))+1/4*2^(1/2)*atan(144/103+148/103*2^(1/2))-1/4*%i*2^(1/2)*atanh(-51945/813577+28/2440731*((714295812*(833932+86508*93^(1/2))^(1/3)-4881462*(833932+86508*93^(1/2))^(2/3)+3963747144)/(833932+86508*93^(1/2))^(1/3))^(1/2)+28/2440731*6^(1/2)*((238098604*(833932+86508*93^(1/2))^(1/3)*((714295812*(833932+86508*93^(1/2))^(1/3)-4881462*(833932+86508*93^(1/2))^(2/3)+3963747144)/(833932+86508*93^(1/2))^(1/3))^(1/2)+813577*((714295812*(833932+86508*93^(1/2))^(1/3)-4881462*(833932+86508*93^(1/2))^(2/3)+3963747144)/(833932+86508*93^(1/2))^(1/3))^(1/2)*(833932+86508*93^(1/2))^(2/3)-660624524*((714295812*(833932+86508*93^(1/2))^(1/3)-4881462*(833932+86508*93^(1/2))^(2/3)+3963747144)/(833932+86508*93^(1/2))^(1/3))^(1/2)+4852325397096*(833932+86508*93^(1/2))^(1/3))/(833932+86508*93^(1/2))^(1/3)/((714295812*(833932+86508*93^(1/2))^(1/3)-4881462*(833932+86508*93^(1/2))^(2/3)+3963747144)/(833932+86508*93^(1/2))^(1/3))^(1/2))^(1/2))+1/8*%i*2^(1/2)*log(18/7)+1/8*log(81*(69/97+2/97*2^(1/2))^(%i*2^(1/2))*((26+7*%i-(10+4*%i)*2^(1/2))*(1/3+1/18*6^(1/2)*((62*(1052+108*93^(1/2))^(1/3)+(1052+108*93^(1/2))^(2/3)+28)/(1052+108*93^(1/2))^(1/3))^(1/2)+1/18*((744*(1052+108*93^(1/2))^(1/3)*((62*(1052+108*93^(1/2))^(1/3)+(1052+108*93^(1/2))^(2/3)+28)/(1052+108*93^(1/2))^(1/3))^(1/2)-6*((62*(1052+108*93^(1/2))^(1/3)+(1052+108*93^(1/2))^(2/3)+28)/(1052+108*93^(1/2))^(1/3))^(1/2)*(1052+108*93^(1/2))^(2/3)-168*((62*(1052+108*93^(1/2))^(1/3)+(1052+108*93^(1/2))^(2/3)+28)/(1052+108*93^(1/2))^(1/3))^(1/2)+2376*6^(1/2)*(1052+108*93^(1/2))^(1/3))/(1052+108*93^(1/2))^(1/3)/((62*(1052+108*93^(1/2))^(1/3)+(1052+108*93^(1/2))^(2/3)+28)/(1052+108*93^(1/2))^(1/3))^(1/2))^(1/2))/(3+2^(1/2)))^(2*%i*2^(1/2))/((2+3*%i-2*%i*2^(1/2))^(4*%i*2^(1/2))))-acoth(2))*2^(1/2));