Using a Let's Encrypt SSL certificate with the Alpine image

I have a problem that's been quite hard to debug. Trying to use a Let's Encrypt certificate, I'm unable to have it play nice with `influxdb:alpine`. The certificate is issued for `*.ourdomain.com` and everything seems to be in order:
```
Data:
Version: 3 (0x2)
Serial Number:
XX:XX:XX:XX:XX:XX:XX:XX:XX:XX:6f:XX:XX:XX:XX:XX:XX:XX
Signature Algorithm: sha256WithRSAEncryption
Issuer: C = US, O = Let's Encrypt, CN = Let's Encrypt Authority X3
Validity
Not Before: Dec 6 16:32:07 2018 GMT
Not After : Mar 6 16:32:07 2019 GMT
Subject: CN = *.ourdomain.com
```

I have loaded a similar certificate on our `chronograf:alpine` image without a problem. The error I am getting from my client:
```
$ influx -ssl -host ts.ourdomain.com
$ Failed to connect to https://ts.ourdomain.com:8086: Get https://ts.ourdomain.com:8086/ping: x509: certificate signed by unknown authority
Please check your connection settings and ensure 'influxd' is running.
```

The error that I am getting from my docker container:
```
2018/12/07 13:19:03 http: TLS handshake error from 79.173.555.555:40786: remote error: tls: bad certificate
```
Any idea where that could come from or how to debug further? Thanks

Start by reproducing the TLS connection against the influxdb:alpine container using the reported influx client command, then compare its certificate setup with the working chronograf:alpine setup. Inspect the container's TLS configuration and certificate chain; done means the source of the unknown-authority and bad-certificate errors is identified and a reproducible configuration fix is documented.

Written by the indexing model from the issue text.