Simplify and express preferentially with tangents : trigtan

trigtan takes as argument an expression containing trigonometric functions.
trigtan simplifies this expression with the formula :
sin(x)2 + cos(x)2 = 1, tan(x) = $${\frac{{\sin(x)}}{{\cos(x)}}}$$ and tries to rewrite the expression only with tangents.
Input :

trigtan(sin(x)^4+cos(x)^2+1)

Output :

((tan(x))^2/(1+(tan(x))^2))^2+1/(1+(tan(x)^2)+1

Output, after simplification with normal :

(2*tan(x)^4+3*tan(x)^2+2)/(tan(x)^4+2*tan(x))^2+1)