How this $\sum_{n=0}^m n^{\exp ( \tan (n\pi))}$ related to Hurwitz zeta function?

Question

I have tried to get this partial sum $\sum_{n=0}^m n^{\exp ( \tan (n\pi))}$ , In the first I have tried instead of $n$ a fixed integer $k$ the series is diverge but the partial sum give me affine function which is $k(m+1)$, But when I tried to take the sum as $\sum_{n=0}^m n^{\exp ( \tan (n\pi))}$ it were hard for me fo evaluation however , Wolfram alpha turned me this result:$$\sum_{n=0}^m n^{\exp ( \tan (n\pi))}=-\zeta(-1,m+1)-\frac{1}{12}$$ related to Hurwitz zeta function but I can't prove it ?