Correlation between frequency and initial phase estimates using FFT

Why is there a high negative correlation between frequency estimation errors and initial phase estimation errors when measured using FFT? I have a simple code showing this negative correlation. is there a known explanation for that? here is the code

clear all;clc;close all;

%%
T = 0.2;
fs = 500;
f = 200;
ts = 1/fs;
snr = 5;
n = fs*T;
t = linspace(0,T-ts,n);
theta = 0.1;
y = exp(1i*2*pi*(f.*t + theta));

for count = 1:2000
    count;
    yy  =  awgn(y,snr,'measured');
    NFFT = 2^16;
    fVals = fs/NFFT.*[0:NFFT-1];
    X = fft(yy,NFFT)./n;
    plot(abs(X))
    [~,M] = findpeaks(abs(X),'MinPeakheight',0.8);
    measuredAngle = angle(X(M))/2/pi;
    errfreq(count) = fVals(M) - f;

    errph(count) = measuredAngle - theta;
end
cov(errfreq,errph)
corrcoef(errfreq,errph)


ans =
    1.0000   -0.8506
   -0.8506    1.0000