Connect the curve 6

We plot two continuous curves $f\left( x \right) =\sin { \left( x+a \right) } \cos { \left( x-a \right) } \\ g\left( x \right) =\sin { \left( x-a \right) } \cos { \left( x+a \right) }$

And another curve $h\left( x \right) =\frac { f\left( x \right) }{ g\left( x \right) }$

It is observed that for some $a$ , such that $\frac { \pi }{ 2 } <a<\pi$ , the curve of $h\left( x \right)$ is tangent to the curve of $f\left( x \right)$ at point $\left( t,h\left( t \right) \right)$ . Here, $0<t<\frac { \pi }{ 2 }$ .

If $t+a$ can be expressed as $\frac { A }{ B } { \pi }^{ C }+D$ such that $gcd\left( A,B \right) =1$ and $A,B,C,D\in Z$ , find the value of $AB+C+D$

Hint: Differentiate